assignment on moment analysis for biomechanics .....write task...phases...joints involved....muscles involved....plane and axis....kinetics....kinematics....functional significance right give me subtopics properly ............ in pointers and tabular form .......for stand to sit

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stand to sit biomechanics moment analysis phases joints muscles kinematics kinetics

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stand to sit biomechanics joint moments eccentric muscle action phases ankle knee hip kinetics

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MOMENT ANALYSIS IN BIOMECHANICS

Movement: STAND TO SIT (StandTS)


1. TASK DEFINITION

  • Stand to Sit (StandTS) is the controlled lowering of the body from an upright standing position to a seated position on a chair or surface.
  • It is a closed-kinetic chain, anti-gravity eccentric movement where muscles actively lengthen to resist gravity.
  • The task demands coordinated multi-joint control to safely transfer body weight from feet to the seat.
  • It is the reverse of Sit-to-Stand but is not simply its mirror - it requires different neuromuscular strategies due to gravity-assisted descent.
  • It occurs hundreds of times per day, making it clinically significant for fall prevention, rehabilitation, and functional independence assessment.

2. PHASES OF STAND TO SIT

PhaseNameEvent MarkerDescription
Phase 1Initiation / Forward LeanStart of trunk flexion forwardTrunk inclines forward; COM shifts anteriorly over BOS; hip flexion begins
Phase 2Descent / Controlled LoweringHip lift-off to just before seat contactEccentric lowering of COM; all lower limb joints flex under load; maximum demands on knee extensors
Phase 3Seat Contact / LoadingButtocks contact the seatBody weight begins transferring from feet to seat; shock absorption
Phase 4Stabilization / SettlingFull seated position achievedPostural muscles stabilize the trunk in sitting; weight fully on seat
Key biomechanical transitions:
  • Maximum trunk flexion occurs early (Phase 1)
  • Peak ground reaction force (GRF) occurs during controlled descent (Phase 2)
  • Maximum knee flexion moment: late Phase 2 / early Phase 3
  • Seat impact forces peak at onset of Phase 3

3. JOINTS INVOLVED

JointPrimary Motion (StandTS)Type of MovementRange
AnkleDorsiflexion (controlled)Eccentric plantarflexors0° to ~15-20° DF
KneeFlexionEccentric knee extensors0° to ~90°-110°
HipFlexionEccentric hip extensors0° to ~80°-100°
Lumbar SpineSlight flexion / anterior tilt of pelvisErector spinae controlControlled flexion
Thoracic SpineFlexion during forward leanPostural stabilizationMild flexion
PelvisAnterior tilt (then posterior tilt at seat)Pelvic control musclesTransitional
Secondary joints:
  • Subtalar joint - minor pronation for shock absorption
  • Glenohumeral joint - arms may be used for balance or support

4. MUSCLES INVOLVED

Primary Muscles (Eccentric Action - controlling descent)

MuscleJoint ControlledAction TypeRole
Quadriceps (Rectus Femoris, Vastus Lateralis, Vastus Medialis, Vastus Intermedius)KneeEccentric (lengthening)Control knee flexion against gravity; dominant muscle group in StandTS
Gluteus MaximusHipEccentricControls hip flexion; prevents uncontrolled forward collapse
Hamstrings (Biceps Femoris, Semimembranosus, Semitendinosus)Hip + KneeEccentric (bi-articular role)Co-stabilize hip and knee; assist hip extension control
Tibialis AnteriorAnkleEccentric (then concentric)Controls dorsiflexion; stabilizes during descent
Soleus / GastrocnemiusAnkleEccentricControl forward tibial progression; resist uncontrolled dorsiflexion
Erector Spinae / MultifidusLumbar spineIsometric/eccentricMaintain trunk alignment; prevent excessive trunk flexion

Stabilizing / Secondary Muscles

MuscleRole
Gluteus MediusFrontal plane pelvic stability; prevents hip adduction/drop
Adductor MagnusHip extensor assist in deeper descent angles
Tibialis PosteriorSubtalar stabilization
Tensor Fasciae Latae (TFL)Assists hip abduction stability
Abdominals (Transversus Abdominis, Obliques)Core stability and trunk control during flexion

5. PLANE AND AXIS OF MOTION

JointPrimary PlaneAxis of RotationMotion Description
KneeSagittal planeFrontal (mediolateral) axisFlexion in sagittal plane
HipSagittal planeFrontal (mediolateral) axisFlexion in sagittal plane
AnkleSagittal planeFrontal (mediolateral) axisDorsiflexion in sagittal plane
TrunkSagittal planeFrontal (mediolateral) axisForward lean / flexion
PelvisSagittal planeFrontal (mediolateral) axisAnterior then posterior tilt
Note on secondary planes:
  • Minor transverse plane rotation at hip (internal/external) can occur
  • Gluteus medius controls frontal plane deviations at hip (coronal plane, A-P axis)
  • Overall, StandTS is predominantly a sagittal plane movement

6. KINEMATICS

Joint Angular Displacement (Stand → Sit)

JointStart (Standing)End (Seated)Peak AngleDirection
Ankle0° (neutral)~15-20° dorsiflexion~20° DFDorsiflexion
Knee0° (full extension)~90-110° flexion~110° at seatFlexion
Hip0° (full extension)~80-100° flexion~100° at seatFlexion
Trunk (forward lean)Upright (~0°)~30-40° forward lean~35° forward leanFlexion

Center of Mass (COM) Trajectory

  • Horizontal displacement: COM moves posteriorly as hips flex, must stay within base of support (BOS)
  • Vertical displacement: COM descends from ~1.0 m to ~0.5 m height (chair height dependent)
  • Velocity: COM velocity increases during descent, decelerated just before seat contact
  • Momentum: Forward horizontal momentum must be controlled to avoid falling backward

Angular Velocity

JointPeak Angular VelocityPhase
Knee~100-150°/sec (descent)Phase 2
Hip~80-120°/secPhase 2
Ankle~40-60°/secPhase 2

Kinematic Sequence

  1. Trunk inclines forward (Phase 1)
  2. Hip flexes, initiating descent
  3. Knee flexes progressively as body lowers
  4. Ankle dorsiflexes as tibia tilts forward
  5. Pelvis rotates posteriorly as seat contact nears
  6. Full flexion at all joints at seat contact

7. KINETICS

Ground Reaction Forces (GRF)

PhaseGRF PatternNotes
Phase 1 (Initiation)~100% body weight (BW)Still in double support standing
Phase 2 (Descent)Gradually decreasing as seat approachedSome load transferred to incoming seat
Phase 3 (Seat Contact)Impact spike possible; GRF drops rapidlySeat takes increasing load
Phase 4 (Settled)Minimal at feetWeight borne by ischial tuberosities on seat

Joint Moments (Net Internal Moments)

JointMoment TypeDirectionPeak ValuePhase
KneeExtension moment (resisting flexion)Extensor~0.8 - 1.2 Nm/kg (highest demand)Phase 2
HipExtension moment (resisting hip flexion)Extensor~0.5 - 0.9 Nm/kgPhase 2
AnklePlantarflexion moment (resisting dorsiflexion)Plantarflexor~0.3 - 0.5 Nm/kgPhase 2
Trunk/LumbarExtensor momentSpinal extensorsHigh during forward leanPhase 1-2

Key Kinetic Principles in StandTS

  • Knee has the highest joint moment demand - vastus lateralis accounts for ~80% of eccentric control
  • Muscle work is negative (eccentric) - energy is absorbed rather than generated
  • Eccentric work at knee > hip > ankle in descending order
  • Seat impact force depends on descent speed - a faster sit produces higher impact forces on spine and hip
  • Newton's 3rd Law: Seat exerts equal and opposite force on body at impact
  • Torque = Force × Perpendicular Distance: Longer moment arm = greater torque demand

Moment Arm Considerations

JointMoment ArmEffect
KneeLargest among lower limb jointsRequires greatest muscle force
HipModerateRequires hip extensor strength
AnkleShortestLeast muscle force needed
Trunk lean forwardIncreases gravitational torque at knee and hipGreater forward lean = greater joint moment demands

8. MOMENT ANALYSIS (Core Section)

Definition

  • Moment (Torque) = Force × Perpendicular Moment Arm
  • In StandTS, gravitational forces create external flexion moments at hip, knee, and ankle
  • Muscles generate internal extension moments to control the rate of descent (eccentric action)

External vs Internal Moments

JointExternal Moment (Gravity)Internal Moment (Muscle)Net Effect
KneeFlexion (gravity pulls body down → knee bends)Extension (quadriceps eccentrically contract)Controlled flexion
HipFlexion (gravity + trunk weight)Extension (gluteus maximus, hamstrings eccentrically)Controlled hip flexion
AnkleDorsiflexion (tibia tilts forward over fixed foot)Plantarflexion (soleus, gastrocnemius eccentrically)Controlled dorsiflexion

Free Body Diagram Concept for Knee (simplified)

  • Body weight (W) acts downward through COM
  • Perpendicular distance from knee joint center to line of gravity = moment arm (d)
  • External knee flexion moment = W × d
  • Quadriceps muscle force (F_q) × quadriceps moment arm (d_q) = Internal knee extension moment
  • At equilibrium: F_q × d_q = W × d → F_q = (W × d) / d_q
  • Since d_q (patellar tendon moment arm) is much smaller than d, F_q is many times greater than W

9. FUNCTIONAL SIGNIFICANCE

AspectSignificance
Daily LivingPerformed hundreds of times daily; decline in ability is a major predictor of functional dependency in elderly
Fall PreventionControlled eccentric strength is essential to prevent uncontrolled dropping into the chair
Knee Extensor StrengthPeak quadriceps eccentric strength directly determines safe StandTS ability; weakness = fall risk
Chair HeightHigher chairs reduce hip/knee moment demands; lower chairs increase them - important in orthopaedic rehab
OsteoarthritisKnee OA patients show altered joint moments and compensatory trunk lean strategies
Post-surgical RehabAfter TKR/THR, StandTS is a benchmark for functional recovery
Neurological ConditionsParkinson's, stroke affect timing and coordination of eccentric muscle control during descent
ObesityIncreased body weight proportionally increases all joint moments
AgingReduced eccentric quadriceps strength with age is primary limiting factor
Clinical Assessment5-times sit-to-stand test (5XSTS) used to assess lower limb strength and fall risk

Compensatory Strategies in Pathological or Weak States

StrategyCompensation ForHow It Helps
Increased trunk lean forwardWeak quadricepsShifts COM forward, reduces knee moment arm
Using armrestsWeak lower limbUpper limb takes partial load
Faster sit (drop)Fatigue / painReduces time of high eccentric demand (but increases impact)
Wider base of supportBalance deficitIncreases stability margins
Hip abductor bracingWeak gluteus mediusPrevents lateral pelvic drop

10. QUICK REFERENCE SUMMARY TABLE

ParameterDetails
MovementStand to Sit (StandTS)
Phases4 phases: Initiation → Descent → Seat Contact → Stabilization
Primary JointsAnkle, Knee, Hip (sagittal plane)
Primary PlaneSagittal
Primary AxisFrontal (Mediolateral)
Primary MusclesQuadriceps (dominant), Gluteus Maximus, Hamstrings, Soleus/Gastroc, Erector Spinae
Muscle Action TypeEccentric (lengthening under load)
KinematicsKnee 0→110° flexion; Hip 0→100° flexion; Ankle 0→20° dorsiflexion
KineticsKnee moment highest (~1.0-1.2 Nm/kg); eccentric work: knee > hip > ankle
COMDescends posteriorly; must remain within BOS throughout
Functional SignificanceFall prevention, rehab benchmark, daily living, aging, OA management

11. APPLIED CLINICAL NOTES (for assignments)

  • Inverse Dynamics method is used clinically to calculate net joint moments from motion capture + force plate data
  • EMG confirms muscle activation patterns - VL shows highest activation in StandTS
  • Moment normalization is done to body weight (Nm/kg) for inter-subject comparison
  • Power analysis: Negative power (energy absorption) at knee and hip during descent = eccentric work
  • Work-Energy Theorem: Negative work done by muscles = kinetic energy of body is absorbed safely
  • Principle of least effort: Humans naturally choose trunk lean angles that minimize peak knee moment

Create a visual PDF with stick diagrams for each StandTS phase

Reading File
Running Command

ls /home/daytona/workspace/ 2>/dev/null && mkdir -p /home/daytona/workspace/stan…

Create a visual PDF with stick diagrams for each StandTS phase

Running Command

mkdir -p /home/daytona/workspace/standts-pdf && python3 -c "import matplotlib; i…

Writing File

~/standts-pdf/generate_standts_pdf.py

"""
Stand-to-Sit Biomechanics - Visual PDF with Stick Diagrams
Generates a professional A4 PDF with annotated stick figures for each StandTS phase.
"""

import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
from matplotlib.patches import FancyArrowPatch, Arc
from matplotlib.lines import Line2D
import numpy as np
from reportlab.lib.pagesizes import A4
from reportlab.lib import colors
from reportlab.lib.units import cm, mm
from reportlab.platypus import (SimpleDocTemplate, Paragraph, Spacer, Image,
                                 Table, TableStyle, HRFlowable, PageBreak)
from reportlab.lib.styles import getSampleStyleSheet, ParagraphStyle
from reportlab.lib.enums import TA_CENTER, TA_LEFT, TA_JUSTIFY
import io
import os

OUT_DIR = "/home/daytona/workspace/standts-pdf"
os.makedirs(OUT_DIR, exist_ok=True)

# ─────────────────────────────────────────────
# COLOUR PALETTE
# ─────────────────────────────────────────────
C_BONE   = "#2C3E50"   # dark navy  – skeleton lines
C_JOINT  = "#E74C3C"   # red        – joint dots
C_HEAD   = "#F39C12"   # amber      – head circle
C_ARROW  = "#27AE60"   # green      – moment/force arrows
C_CHAIR  = "#95A5A6"   # grey       – chair
C_FLOOR  = "#7F8C8D"   # darker grey– floor
C_SHADE  = "#EBF5FB"   # light blue – panel bg
C_ACCENT = "#2980B9"   # blue       – accent lines
C_MUSCLE = "#8E44AD"   # purple     – muscle label arrows
C_GRF    = "#E67E22"   # orange     – GRF arrow

PHASE_COLORS = ["#1ABC9C", "#3498DB", "#E74C3C", "#9B59B6"]

# ─────────────────────────────────────────────
# STICK FIGURE DRAWING HELPER
# ─────────────────────────────────────────────

def draw_stick_figure(ax, joints, chair_h=None, show_chair=True,
                       grf_arrow=True, moment_joints=None,
                       muscle_labels=None, com_pos=None,
                       angle_labels=None):
    """
    joints: dict with keys = joint names, values = (x, y) in axis units
    Expected keys: ankle, knee, hip, shoulder, elbow, wrist, neck, head_c
                   also: foot_heel, foot_toe
    """
    ax.set_xlim(-1.2, 1.8)
    ax.set_ylim(-0.15, 2.3)
    ax.set_aspect('equal')
    ax.axis('off')
    ax.set_facecolor(C_SHADE)

    lw = 3.2   # bone line width
    js = 80    # joint scatter size

    # ── Floor ──
    ax.axhline(0, color=C_FLOOR, lw=2.5, zorder=0)
    ax.fill_between([-1.2, 1.8], [-0.15, -0.15], [0, 0],
                    color="#BDC3C7", alpha=0.5, zorder=0)

    # ── Chair ──
    if show_chair and chair_h is not None:
        seat_y = chair_h
        seat_x0, seat_x1 = -0.05, 0.85
        back_x = seat_x0
        # seat surface
        ax.plot([seat_x0, seat_x1], [seat_y, seat_y],
                color=C_CHAIR, lw=5, solid_capstyle='round', zorder=1)
        # seat back
        ax.plot([back_x, back_x], [seat_y, seat_y + 0.55],
                color=C_CHAIR, lw=5, solid_capstyle='round', zorder=1)
        # legs
        for lx in [seat_x0 + 0.05, seat_x1 - 0.05]:
            ax.plot([lx, lx], [0, seat_y],
                    color=C_CHAIR, lw=3, zorder=1)

    j = joints  # shorthand

    def bone(a, b, **kw):
        ax.plot([j[a][0], j[b][0]], [j[a][1], j[b][1]],
                color=kw.get('color', C_BONE),
                lw=kw.get('lw', lw),
                solid_capstyle='round', zorder=3)

    # ── Skeleton segments ──
    # Foot
    bone('foot_heel', 'ankle')
    bone('ankle', 'foot_toe')
    # Lower leg
    bone('ankle', 'knee')
    # Upper leg
    bone('knee', 'hip')
    # Trunk
    bone('hip', 'shoulder')
    # Upper arm
    bone('shoulder', 'elbow')
    # Forearm
    bone('elbow', 'wrist')
    # Neck
    bone('shoulder', 'neck')

    # ── Head ──
    head_r = 0.10
    head = plt.Circle(j['head_c'], head_r, color=C_HEAD,
                       ec=C_BONE, lw=1.5, zorder=4)
    ax.add_patch(head)

    # ── Joints ──
    joint_pts = ['ankle', 'knee', 'hip', 'shoulder', 'elbow', 'wrist', 'neck']
    xs = [j[k][0] for k in joint_pts]
    ys = [j[k][1] for k in joint_pts]
    ax.scatter(xs, ys, s=js, color=C_JOINT, zorder=5, edgecolors='white', lw=1)

    # ── GRF Arrow ──
    if grf_arrow:
        ankle_x = j['ankle'][0]
        grf_h = 0.55
        ax.annotate("", xy=(ankle_x, grf_h), xytext=(ankle_x, 0),
                    arrowprops=dict(arrowstyle="-|>",
                                   color=C_GRF, lw=2.2,
                                   mutation_scale=18))
        ax.text(ankle_x + 0.12, grf_h / 2, "GRF",
                color=C_GRF, fontsize=7, fontweight='bold', va='center')

    # ── COM marker ──
    if com_pos:
        ax.plot(com_pos[0], com_pos[1], marker='*', markersize=14,
                color=C_ACCENT, zorder=6,
                markeredgecolor='white', markeredgewidth=0.8)
        ax.text(com_pos[0] + 0.12, com_pos[1],
                "COM", color=C_ACCENT, fontsize=7, fontweight='bold', va='center')

    # ── Moment arcs ──
    if moment_joints:
        for mj, direction, label in moment_joints:
            cx, cy = j[mj]
            r = 0.22
            t1, t2 = (20, 160) if direction == 'ext' else (200, 340)
            arc = Arc((cx, cy), 2*r, 2*r, angle=0,
                      theta1=t1, theta2=t2,
                      color=C_ARROW, lw=2, zorder=6)
            ax.add_patch(arc)
            # arrowhead at end of arc
            mid_ang = np.radians((t1 + t2) / 2)
            ax.text(cx + (r+0.07)*np.cos(mid_ang),
                    cy + (r+0.07)*np.sin(mid_ang),
                    label, color=C_ARROW, fontsize=6.5,
                    fontweight='bold', ha='center', va='center')

    # ── Angle labels ──
    if angle_labels:
        for jname, angle_txt, offset in angle_labels:
            cx, cy = j[jname]
            ax.text(cx + offset[0], cy + offset[1],
                    angle_txt, color="#2C3E50",
                    fontsize=6.5, ha='center', va='center',
                    bbox=dict(boxstyle='round,pad=0.2',
                              fc='white', ec='#BDC3C7', alpha=0.85))

    # ── Muscle labels ──
    if muscle_labels:
        for mname, pos, jname in muscle_labels:
            mx, my = pos
            jx, jy = j[jname]
            ax.annotate(mname,
                        xy=(jx, jy), xytext=(mx, my),
                        fontsize=6, color=C_MUSCLE, fontweight='bold',
                        arrowprops=dict(arrowstyle='-',
                                        color=C_MUSCLE, lw=1.2,
                                        linestyle='dashed'),
                        ha='center', va='center',
                        bbox=dict(boxstyle='round,pad=0.15',
                                  fc='#F8F9FA', ec=C_MUSCLE, alpha=0.9))


# ─────────────────────────────────────────────
# DEFINE JOINT POSITIONS FOR EACH PHASE
# ─────────────────────────────────────────────

CHAIR_H = 0.52   # seat height

def phase1_joints():
    """Phase 1: Standing upright, just beginning forward trunk lean"""
    ankle  = (0.30, 0.08)
    knee   = (0.30, 0.58)
    hip    = (0.30, 1.05)
    # Trunk leans ~15° forward
    trunk_len = 0.50
    trunk_angle = np.radians(80)  # nearly upright, slight lean
    shoulder = (hip[0] + trunk_len * np.cos(np.pi/2 - np.radians(10)),
                hip[1] + trunk_len * np.sin(np.pi/2 - np.radians(10)))
    neck  = (shoulder[0] + 0.00, shoulder[1] + 0.10)
    head_c = (neck[0] + 0.01, neck[1] + 0.20)
    elbow  = (shoulder[0] + 0.18, shoulder[1] - 0.18)
    wrist  = (shoulder[0] + 0.30, shoulder[1] - 0.35)
    foot_heel = (ankle[0] - 0.15, 0.01)
    foot_toe  = (ankle[0] + 0.18, 0.01)
    return dict(ankle=ankle, knee=knee, hip=hip, shoulder=shoulder,
                neck=neck, head_c=head_c, elbow=elbow, wrist=wrist,
                foot_heel=foot_heel, foot_toe=foot_toe)

def phase2_joints():
    """Phase 2: Controlled descent - trunk inclined, knees bent ~45°"""
    ankle  = (0.28, 0.08)
    knee   = (0.42, 0.52)
    hip    = (0.20, 0.92)
    # Trunk leaning ~30° forward
    trunk_len = 0.50
    shoulder = (hip[0] + trunk_len * np.sin(np.radians(30)),
                hip[1] + trunk_len * np.cos(np.radians(30)))
    neck   = (shoulder[0] + 0.02, shoulder[1] + 0.10)
    head_c = (neck[0] + 0.04, neck[1] + 0.19)
    elbow  = (shoulder[0] + 0.12, shoulder[1] - 0.20)
    wrist  = (shoulder[0] + 0.18, shoulder[1] - 0.38)
    foot_heel = (ankle[0] - 0.15, 0.01)
    foot_toe  = (ankle[0] + 0.18, 0.01)
    return dict(ankle=ankle, knee=knee, hip=hip, shoulder=shoulder,
                neck=neck, head_c=head_c, elbow=elbow, wrist=wrist,
                foot_heel=foot_heel, foot_toe=foot_toe)

def phase3_joints():
    """Phase 3: Seat contact - buttocks touching chair, knees ~90°"""
    ankle  = (0.25, 0.08)
    knee   = (0.55, 0.50)
    hip    = (0.42, CHAIR_H)
    # Trunk more upright after seat contact
    trunk_len = 0.52
    shoulder = (hip[0] + trunk_len * np.sin(np.radians(20)),
                hip[1] + trunk_len * np.cos(np.radians(20)))
    neck   = (shoulder[0] + 0.00, shoulder[1] + 0.10)
    head_c = (neck[0] + 0.02, neck[1] + 0.19)
    elbow  = (shoulder[0] + 0.10, shoulder[1] - 0.22)
    wrist  = (shoulder[0] + 0.14, shoulder[1] - 0.40)
    foot_heel = (ankle[0] - 0.14, 0.01)
    foot_toe  = (ankle[0] + 0.18, 0.01)
    return dict(ankle=ankle, knee=knee, hip=hip, shoulder=shoulder,
                neck=neck, head_c=head_c, elbow=elbow, wrist=wrist,
                foot_heel=foot_heel, foot_toe=foot_toe)

def phase4_joints():
    """Phase 4: Fully seated, stabilized upright"""
    ankle  = (0.22, 0.08)
    knee   = (0.58, 0.50)
    hip    = (0.50, CHAIR_H + 0.02)
    # Trunk upright
    trunk_len = 0.54
    shoulder = (hip[0] + trunk_len * np.sin(np.radians(5)),
                hip[1] + trunk_len * np.cos(np.radians(5)))
    neck   = (shoulder[0] + 0.00, shoulder[1] + 0.10)
    head_c = (neck[0] + 0.01, neck[1] + 0.19)
    elbow  = (shoulder[0] - 0.12, shoulder[1] - 0.18)
    wrist  = (shoulder[0] - 0.20, shoulder[1] - 0.35)
    foot_heel = (ankle[0] - 0.12, 0.01)
    foot_toe  = (ankle[0] + 0.18, 0.01)
    return dict(ankle=ankle, knee=knee, hip=hip, shoulder=shoulder,
                neck=neck, head_c=head_c, elbow=elbow, wrist=wrist,
                foot_heel=foot_heel, foot_toe=foot_toe)

# ─────────────────────────────────────────────
# PHASE METADATA
# ─────────────────────────────────────────────

PHASES = [
    {
        "num": 1,
        "name": "Phase 1 – Initiation / Forward Lean",
        "joints_fn": phase1_joints,
        "show_chair": True,
        "grf": True,
        "com": (0.62, 1.10),
        "moments": [
            ("knee", "ext", "Ext\nMoment"),
            ("hip",  "ext", "Ext\nMoment"),
        ],
        "muscles": [
            ("Quadriceps\n(begin eccentric)", (-0.55, 0.85), "knee"),
            ("Glut. Max\n(begin eccentric)", (-0.55, 1.30), "hip"),
            ("Erector\nSpinae", (1.30, 1.50), "shoulder"),
        ],
        "angles": [
            ("knee", "~0°\nknee flex", (0.30, 0.35)),
            ("hip",  "~5°\nhip flex",  (0.62, 1.05)),
            ("ankle","~0°\nneutral",   (-0.15, 0.25)),
        ],
        "color": PHASE_COLORS[0],
        "key_points": [
            "Trunk begins to incline forward",
            "COM shifts anteriorly over BOS",
            "Minimal joint flexion at start",
            "Erector spinae active isometrically",
            "GRF = ~100% body weight (BW)",
            "Quadriceps begin eccentric pre-activation",
        ],
        "kinetics": "GRF ≈ 100% BW | Knee moment: low | Hip moment: low",
        "kinematics": "Knee: 0° | Hip: 0-5° flex | Ankle: neutral",
        "muscle_action": "Eccentric activation begins (quads, glut max)",
    },
    {
        "num": 2,
        "name": "Phase 2 – Controlled Descent",
        "joints_fn": phase2_joints,
        "show_chair": True,
        "grf": True,
        "com": (0.52, 1.02),
        "moments": [
            ("knee", "ext", "PEAK\nExt Moment"),
            ("hip",  "ext", "Ext\nMoment"),
            ("ankle","ext", "PF\nMoment"),
        ],
        "muscles": [
            ("Quadriceps\n(MAX eccentric)", (-0.60, 0.70), "knee"),
            ("Glut. Max\n(eccentric)", (-0.60, 1.10), "hip"),
            ("Soleus\n(eccentric)", (-0.60, 0.35), "ankle"),
        ],
        "angles": [
            ("knee", "~45-70°\nknee flex", (0.65, 0.38)),
            ("hip",  "~50°\nhip flex",    (0.60, 0.88)),
            ("ankle","~15°\ndorsiflexion",(−0.18, 0.28)),
        ],
        "color": PHASE_COLORS[1],
        "key_points": [
            "Body actively lowering toward chair",
            "PEAK knee extensor eccentric moment",
            "COM descends and moves posteriorly",
            "Quadriceps = dominant muscle (~80% eccentric control)",
            "Tibial forward lean drives ankle dorsiflexion",
            "GRF begins to decrease as seat approached",
        ],
        "kinetics": "GRF decreasing | Knee moment: PEAK ~1.0-1.2 Nm/kg | Hip: ~0.7 Nm/kg",
        "kinematics": "Knee: 45-70° flex | Hip: 40-60° flex | Ankle: 10-18° DF",
        "muscle_action": "All lower limb muscles ECCENTRICALLY active (quads dominant)",
    },
    {
        "num": 3,
        "name": "Phase 3 – Seat Contact / Loading",
        "joints_fn": phase3_joints,
        "show_chair": True,
        "grf": True,
        "com": (0.68, 1.00),
        "moments": [
            ("knee", "ext", "Ext\nMoment"),
            ("hip",  "ext", "Ext\nMoment"),
        ],
        "muscles": [
            ("Quadriceps\n(eccentric→iso)", (-0.58, 0.65), "knee"),
            ("Hamstrings\n(co-activation)", (1.30, 0.68), "knee"),
            ("Hip Flexors\n(stabilize)",    (1.30, 1.05), "hip"),
        ],
        "angles": [
            ("knee", "~90°\nknee flex", (0.72, 0.32)),
            ("hip",  "~85°\nhip flex",  (0.68, 0.70)),
            ("ankle","~18°\ndorsiflexion", (-0.18, 0.25)),
        ],
        "color": PHASE_COLORS[2],
        "key_points": [
            "Buttocks make contact with seat surface",
            "Weight rapidly transferring: feet → ischial tuberosities",
            "GRF drops sharply at feet as seat bears load",
            "Impact forces at hip/spine depend on descent speed",
            "Quadriceps transition eccentric → isometric",
            "Hamstrings co-activate for knee stability",
        ],
        "kinetics": "GRF drops at feet | Seat impact force peaks | Knee ~90° load",
        "kinematics": "Knee: ~90° | Hip: ~80-90° flex | Ankle: ~18-20° DF",
        "muscle_action": "Eccentric → Isometric transition; hamstrings co-activate",
    },
    {
        "num": 4,
        "name": "Phase 4 – Stabilization / Fully Seated",
        "joints_fn": phase4_joints,
        "show_chair": True,
        "grf": False,
        "com": (0.72, 1.10),
        "moments": None,
        "muscles": [
            ("Postural\nMuscles (iso)",  (-0.58, 1.40), "shoulder"),
            ("Hip Abductors\n(stabilize)", (1.30, 0.82), "hip"),
            ("Tibialis Ant.\n(stabilize)", (-0.60, 0.40), "ankle"),
        ],
        "angles": [
            ("knee", "~90-110°\nknee flex", (0.72, 0.28)),
            ("hip",  "~90-100°\nhip flex",  (0.72, 0.72)),
        ],
        "color": PHASE_COLORS[3],
        "key_points": [
            "Full seated position achieved",
            "Body weight borne by ischial tuberosities on seat",
            "GRF at feet ≈ minimal",
            "Postural muscles maintain upright trunk (isometric)",
            "Hip abductors prevent pelvic drop",
            "Trunk erectors maintain spinal alignment",
        ],
        "kinetics": "GRF at feet ≈ minimal | Weight on seat | All moments low",
        "kinematics": "Knee: ~90-110° | Hip: ~90-100° | Ankle: relaxed",
        "muscle_action": "Isometric postural stabilization; eccentric work complete",
    },
]


# ─────────────────────────────────────────────
# GENERATE INDIVIDUAL PHASE FIGURE → PNG bytes
# ─────────────────────────────────────────────

def make_phase_figure(phase_data, width_in=7.5, height_in=4.0):
    fig = plt.figure(figsize=(width_in, height_in), facecolor='white')
    fig.patch.set_facecolor('white')

    # Layout: stick fig (left) | info panel (right)
    gs = fig.add_gridspec(1, 2, width_ratios=[1, 1.6],
                          left=0.02, right=0.98,
                          top=0.92, bottom=0.04, wspace=0.08)

    ax_fig = fig.add_subplot(gs[0])
    ax_txt = fig.add_subplot(gs[1])

    phase_color = phase_data["color"]

    # ── Phase title banner ──
    fig.text(0.5, 0.97, phase_data["name"],
             ha='center', va='top', fontsize=13, fontweight='bold',
             color='white',
             bbox=dict(boxstyle='round,pad=0.4', fc=phase_color,
                       ec='none', alpha=0.95),
             transform=fig.transFigure)

    # ── Stick figure ──
    j = phase_data["joints_fn"]()
    draw_stick_figure(
        ax_fig, j,
        chair_h=CHAIR_H,
        show_chair=phase_data["show_chair"],
        grf_arrow=phase_data["grf"],
        moment_joints=phase_data["moments"],
        muscle_labels=phase_data["muscles"],
        com_pos=phase_data["com"],
        angle_labels=phase_data["angles"],
    )

    # Phase number watermark in figure panel
    ax_fig.text(0.02, 0.97, f"P{phase_data['num']}",
                transform=ax_fig.transAxes,
                fontsize=22, fontweight='black',
                color=phase_color, alpha=0.25,
                va='top', ha='left')

    # ── Info panel ──
    ax_txt.axis('off')
    ax_txt.set_facecolor('white')

    # Key Points box
    y = 0.97
    ax_txt.text(0.03, y, "KEY EVENTS", transform=ax_txt.transAxes,
                fontsize=8.5, fontweight='bold', color=phase_color, va='top')
    y -= 0.09
    for pt in phase_data["key_points"]:
        ax_txt.text(0.03, y, f"  • {pt}", transform=ax_txt.transAxes,
                    fontsize=7.2, color='#2C3E50', va='top')
        y -= 0.085

    y -= 0.04

    def info_block(label, value, ypos, color):
        ax_txt.text(0.03, ypos, label, transform=ax_txt.transAxes,
                    fontsize=7.5, fontweight='bold', color=color, va='top')
        ax_txt.text(0.03, ypos - 0.09, value, transform=ax_txt.transAxes,
                    fontsize=7, color='#34495E', va='top',
                    wrap=True)
        return ypos - 0.19

    y = info_block("KINETICS", phase_data["kinetics"], y, "#E74C3C")
    y = info_block("KINEMATICS", phase_data["kinematics"], y, "#2980B9")
    y = info_block("MUSCLE ACTION", phase_data["muscle_action"], y, "#8E44AD")

    # ── Legend ──
    legend_items = [
        mpatches.Patch(color=C_JOINT,  label='Joint'),
        mpatches.Patch(color=C_HEAD,   label='Head'),
        mpatches.Patch(color=C_GRF,    label='GRF Arrow'),
        mpatches.Patch(color=C_ARROW,  label='Net Moment Arc'),
        mpatches.Patch(color=C_ACCENT, label='COM (★)'),
        mpatches.Patch(color=C_MUSCLE, label='Muscle Label'),
    ]
    ax_txt.legend(handles=legend_items, loc='lower left',
                  fontsize=6, framealpha=0.9, ncol=2,
                  bbox_to_anchor=(0.0, 0.0))

    buf = io.BytesIO()
    fig.savefig(buf, format='png', dpi=180, bbox_inches='tight',
                facecolor='white')
    plt.close(fig)
    buf.seek(0)
    return buf.read()


# ─────────────────────────────────────────────
# GENERATE OVERVIEW COMPARISON FIGURE (all 4)
# ─────────────────────────────────────────────

def make_overview_figure():
    fig, axes = plt.subplots(1, 4, figsize=(14, 4.5),
                              facecolor='white')
    fig.patch.set_facecolor('white')
    fig.suptitle("Stand-to-Sit (StandTS) – 4-Phase Overview",
                 fontsize=14, fontweight='bold', color='#2C3E50', y=1.01)

    phase_fns = [phase1_joints, phase2_joints, phase3_joints, phase4_joints]
    labels = ["Phase 1\nInitiation", "Phase 2\nDescent",
              "Phase 3\nSeat Contact", "Phase 4\nStabilization"]
    grf_flags = [True, True, True, False]

    for i, (ax, fn, lbl, grf, pc) in enumerate(
            zip(axes, phase_fns, labels, grf_flags, PHASE_COLORS)):
        j = fn()
        moments = None
        if i == 1:  # Phase 2 - show peak moment
            moments = [("knee", "ext", "PEAK")]
        draw_stick_figure(ax, j, chair_h=CHAIR_H, show_chair=True,
                          grf_arrow=grf, moment_joints=moments,
                          muscle_labels=None, com_pos=None,
                          angle_labels=None)
        ax.set_title(lbl, fontsize=9, fontweight='bold',
                     color='white', pad=4,
                     bbox=dict(boxstyle='round,pad=0.3',
                               fc=pc, ec='none'))

    # Arrow connecting phases
    for i in range(3):
        fig.add_artist(mpatches.FancyArrowPatch(
            ((i + 1) * 0.25 - 0.01, 0.5), ((i + 1) * 0.25 + 0.01, 0.5),
            arrowstyle='-|>', mutation_scale=18,
            color='#95A5A6', lw=1.5,
            transform=fig.transFigure, figure=fig))

    plt.tight_layout(pad=0.5)
    buf = io.BytesIO()
    fig.savefig(buf, format='png', dpi=180, bbox_inches='tight',
                facecolor='white')
    plt.close(fig)
    buf.seek(0)
    return buf.read()


# ─────────────────────────────────────────────
# MOMENT SUMMARY CHART
# ─────────────────────────────────────────────

def make_moment_chart():
    fig, ax = plt.subplots(figsize=(8, 3.5), facecolor='white')
    fig.patch.set_facecolor('white')

    phases_x = ["Phase 1\nInitiation", "Phase 2\nDescent",
                 "Phase 3\nSeat Contact", "Phase 4\nStabilization"]
    knee_moments  = [0.15, 1.10, 0.60, 0.05]
    hip_moments   = [0.10, 0.75, 0.45, 0.03]
    ankle_moments = [0.05, 0.40, 0.20, 0.02]

    x = np.arange(len(phases_x))
    w = 0.26

    b1 = ax.bar(x - w, knee_moments,  w, label='Knee Extensor Moment',
                color='#E74C3C', alpha=0.88, edgecolor='white')
    b2 = ax.bar(x,     hip_moments,   w, label='Hip Extensor Moment',
                color='#3498DB', alpha=0.88, edgecolor='white')
    b3 = ax.bar(x + w, ankle_moments, w, label='Ankle Plantarflexor Moment',
                color='#27AE60', alpha=0.88, edgecolor='white')

    ax.set_xticks(x)
    ax.set_xticklabels(phases_x, fontsize=8)
    ax.set_ylabel("Net Joint Moment (Nm/kg)", fontsize=9)
    ax.set_title("Joint Moment Demands Across StandTS Phases",
                 fontsize=11, fontweight='bold', color='#2C3E50')
    ax.legend(fontsize=8, loc='upper right')
    ax.set_ylim(0, 1.4)
    ax.yaxis.grid(True, alpha=0.4, linestyle='--')
    ax.set_facecolor('#F8F9FA')
    ax.spines['top'].set_visible(False)
    ax.spines['right'].set_visible(False)

    # Annotate peak
    ax.annotate("PEAK\nKnee Moment",
                xy=(1 - w, 1.10), xytext=(0.5, 1.25),
                fontsize=7.5, color='#E74C3C', fontweight='bold',
                arrowprops=dict(arrowstyle='-|>', color='#E74C3C', lw=1.5))

    plt.tight_layout()
    buf = io.BytesIO()
    fig.savefig(buf, format='png', dpi=180, bbox_inches='tight',
                facecolor='white')
    plt.close(fig)
    buf.seek(0)
    return buf.read()


# ─────────────────────────────────────────────
# BUILD PDF
# ─────────────────────────────────────────────

def build_pdf(out_path):
    doc = SimpleDocTemplate(
        out_path,
        pagesize=A4,
        leftMargin=1.5*cm, rightMargin=1.5*cm,
        topMargin=1.8*cm,  bottomMargin=1.5*cm,
        title="Stand-to-Sit Biomechanics – Moment Analysis",
        author="Biomechanics Assignment",
    )

    styles = getSampleStyleSheet()
    W = A4[0] - 3*cm   # usable width

    def H(tag, txt):
        style = ParagraphStyle(
            tag,
            fontSize={'h1':16,'h2':12,'h3':10,'body':8.5,'small':7.5}[tag],
            leading={'h1':20,'h2':16,'h3':14,'body':12,'small':10}[tag],
            textColor={'h1':'#2C3E50','h2':'#2980B9','h3':'#8E44AD',
                       'body':'#34495E','small':'#7F8C8D'}[tag],
            fontName={'h1':'Helvetica-Bold','h2':'Helvetica-Bold',
                      'h3':'Helvetica-Bold','body':'Helvetica',
                      'small':'Helvetica'}[tag],
            spaceAfter={'h1':8,'h2':6,'h3':4,'body':4,'small':3}[tag],
            alignment=TA_LEFT,
        )
        return Paragraph(txt, style)

    def centre_img(png_bytes, w_cm=None, h_cm=None):
        buf = io.BytesIO(png_bytes)
        img = Image(buf)
        if w_cm:
            img.drawWidth  = w_cm * cm
            img.drawHeight = (img.imageHeight / img.imageWidth) * w_cm * cm
        if h_cm:
            img.drawHeight = h_cm * cm
            img.drawWidth  = (img.imageWidth / img.imageHeight) * h_cm * cm
        return img

    CENTER = ParagraphStyle('center', parent=styles['Normal'],
                             alignment=TA_CENTER, fontSize=8,
                             textColor=colors.HexColor('#7F8C8D'))
    TITLE_STYLE = ParagraphStyle('title', fontSize=20, fontName='Helvetica-Bold',
                                  textColor=colors.HexColor('#2C3E50'),
                                  alignment=TA_CENTER, spaceAfter=6)
    SUB_STYLE   = ParagraphStyle('sub',   fontSize=11, fontName='Helvetica',
                                  textColor=colors.HexColor('#7F8C8D'),
                                  alignment=TA_CENTER, spaceAfter=4)

    story = []

    # ── COVER / TITLE ──
    story.append(Spacer(1, 1.5*cm))
    story.append(Paragraph("STAND-TO-SIT (StandTS)", TITLE_STYLE))
    story.append(Paragraph("Moment Analysis in Biomechanics", TITLE_STYLE))
    story.append(Spacer(1, 0.3*cm))
    story.append(Paragraph("Visual Guide with Stick Diagrams — Phase-by-Phase Analysis",
                            SUB_STYLE))
    story.append(HRFlowable(width='100%', thickness=2,
                             color=colors.HexColor('#2980B9'),
                             spaceAfter=8))
    story.append(Spacer(1, 0.4*cm))

    # ── OVERVIEW FIGURE ──
    story.append(H('h2', "Phase Overview: Stand → Sit"))
    story.append(Spacer(1, 0.2*cm))
    overview_png = make_overview_figure()
    story.append(centre_img(overview_png, w_cm=17))
    story.append(Paragraph(
        "Figure 1: All four phases of Stand-to-Sit showing stick figure postures, "
        "ground reaction force (GRF) arrows, and peak moment arc (Phase 2).",
        CENTER))
    story.append(Spacer(1, 0.4*cm))

    # ── PHASE OVERVIEW TABLE ──
    story.append(H('h2', "Phase Summary Table"))
    tbl_data = [
        ["Phase", "Name", "Trigger Event", "Key Joint Motion", "Dominant Muscle Action"],
        ["1", "Initiation /\nForward Lean",
         "Start of trunk\nincline forward",
         "Hip flex begins;\nKnee neutral",
         "Eccentric pre-activation\n(quads, glut max)"],
        ["2", "Controlled\nDescent",
         "Hip lift-off to\npre-seat contact",
         "Knee: 0→70° flex\nHip: 0→60° flex\nAnkle: 0→18° DF",
         "PEAK eccentric:\nQuadriceps (~80%)\nGlut. Max, Soleus"],
        ["3", "Seat Contact /\nLoading",
         "Buttocks touch seat\nto weight transfer",
         "Knee: ~90° flex\nHip: ~90° flex",
         "Eccentric → Isometric\nHamstrings co-activate"],
        ["4", "Stabilization /\nSettling",
         "Full seated position\nachieved",
         "All joints stable\nat full flexion",
         "Isometric postural\nstabilization"],
    ]

    tbl = Table(tbl_data, colWidths=[1.0*cm, 2.8*cm, 3.2*cm, 3.8*cm, 4.2*cm])
    tbl.setStyle(TableStyle([
        ('BACKGROUND',   (0,0), (-1,0), colors.HexColor('#2980B9')),
        ('TEXTCOLOR',    (0,0), (-1,0), colors.white),
        ('FONTNAME',     (0,0), (-1,0), 'Helvetica-Bold'),
        ('FONTSIZE',     (0,0), (-1,0), 8),
        ('ALIGN',        (0,0), (-1,-1), 'CENTER'),
        ('VALIGN',       (0,0), (-1,-1), 'MIDDLE'),
        ('FONTSIZE',     (0,1), (-1,-1), 7.5),
        ('ROWBACKGROUNDS',(0,1),(-1,-1),
         [colors.HexColor('#EBF5FB'), colors.white]),
        ('GRID',         (0,0), (-1,-1), 0.5, colors.HexColor('#BDC3C7')),
        ('TOPPADDING',   (0,0), (-1,-1), 5),
        ('BOTTOMPADDING',(0,0), (-1,-1), 5),
        ('BACKGROUND',   (0,2), (-1,2), colors.HexColor('#D6EAF8')),  # highlight phase 2
    ]))
    story.append(tbl)
    story.append(Spacer(1, 0.5*cm))

    # ── INDIVIDUAL PHASE PAGES ──
    for pd_ in PHASES:
        story.append(PageBreak())
        story.append(H('h2', pd_["name"]))
        story.append(HRFlowable(width='100%', thickness=1.5,
                                 color=colors.HexColor(pd_["color"]),
                                 spaceAfter=6))
        phase_png = make_phase_figure(pd_)
        story.append(centre_img(phase_png, w_cm=16.5))
        story.append(Paragraph(
            f"Figure: Phase {pd_['num']} – {pd_['name'].split('–')[1].strip()}. "
            "Stick figure shows joint positions, net moment arcs (green), "
            "GRF arrow (orange), COM (★ blue), and eccentric muscle labels (purple).",
            CENTER))
        story.append(Spacer(1, 0.3*cm))

        # Detail table per phase
        detail_data = [
            ["KINETICS", pd_["kinetics"]],
            ["KINEMATICS", pd_["kinematics"]],
            ["MUSCLE ACTION", pd_["muscle_action"]],
        ]
        dt = Table(detail_data, colWidths=[3.5*cm, 12.5*cm])
        dt.setStyle(TableStyle([
            ('FONTNAME',  (0,0), (0,-1), 'Helvetica-Bold'),
            ('FONTSIZE',  (0,0), (-1,-1), 8),
            ('TEXTCOLOR', (0,0), (0,-1), colors.HexColor(pd_["color"])),
            ('GRID',      (0,0), (-1,-1), 0.5, colors.HexColor('#D5D8DC')),
            ('VALIGN',    (0,0), (-1,-1), 'MIDDLE'),
            ('TOPPADDING',(0,0), (-1,-1), 5),
            ('BOTTOMPADDING',(0,0), (-1,-1), 5),
            ('ROWBACKGROUNDS',(0,0),(-1,-1),
             [colors.HexColor('#FDFEFE'), colors.HexColor('#EBF5FB'),
              colors.HexColor('#F4ECF7')]),
        ]))
        story.append(dt)

    # ── MOMENT CHART PAGE ──
    story.append(PageBreak())
    story.append(H('h2', "Joint Moment Analysis – Across All Phases"))
    story.append(HRFlowable(width='100%', thickness=1.5,
                             color=colors.HexColor('#E74C3C'), spaceAfter=6))
    moment_png = make_moment_chart()
    story.append(centre_img(moment_png, w_cm=16))
    story.append(Paragraph(
        "Figure: Net joint moment estimates (Nm/kg body mass) at knee, hip, and ankle "
        "across the four StandTS phases. Phase 2 shows the highest demands, particularly "
        "at the knee (peak ~1.0–1.2 Nm/kg). Values are approximate normative references.",
        CENTER))
    story.append(Spacer(1, 0.5*cm))

    # Moment analysis table
    story.append(H('h3', "Moment Analysis Summary Table"))
    ma_data = [
        ["Joint", "External Moment\n(Gravity)", "Internal Moment\n(Muscle)", "Peak Phase", "Peak Value"],
        ["Knee",  "Flexion moment\n(gravity-driven)",
         "Extension moment\n(Quadriceps eccentric)", "Phase 2", "~1.0–1.2 Nm/kg"],
        ["Hip",   "Flexion moment\n(BW + trunk load)",
         "Extension moment\n(Glut Max, Hamstrings)", "Phase 2", "~0.5–0.9 Nm/kg"],
        ["Ankle", "Dorsiflexion moment\n(tibia forward lean)",
         "Plantarflexion moment\n(Soleus, Gastroc)", "Phase 2", "~0.3–0.5 Nm/kg"],
        ["Trunk", "Flexion moment\n(forward lean gravity)",
         "Extension moment\n(Erector Spinae)", "Phase 1–2", "High (variable)"],
    ]
    mat = Table(ma_data, colWidths=[2.2*cm, 4.0*cm, 4.0*cm, 2.5*cm, 3.3*cm])
    mat.setStyle(TableStyle([
        ('BACKGROUND',   (0,0), (-1,0), colors.HexColor('#E74C3C')),
        ('TEXTCOLOR',    (0,0), (-1,0), colors.white),
        ('FONTNAME',     (0,0), (-1,0), 'Helvetica-Bold'),
        ('FONTSIZE',     (0,0), (-1,0), 8),
        ('ALIGN',        (0,0), (-1,-1), 'CENTER'),
        ('VALIGN',       (0,0), (-1,-1), 'MIDDLE'),
        ('FONTSIZE',     (0,1), (-1,-1), 7.5),
        ('ROWBACKGROUNDS',(0,1),(-1,-1),
         [colors.HexColor('#FDEDEC'), colors.white]),
        ('GRID',         (0,0), (-1,-1), 0.5, colors.HexColor('#BDC3C7')),
        ('TOPPADDING',   (0,0), (-1,-1), 5),
        ('BOTTOMPADDING',(0,0), (-1,-1), 5),
    ]))
    story.append(mat)
    story.append(Spacer(1, 0.5*cm))

    # Key Equations box
    story.append(H('h3', "Key Biomechanical Equations"))
    eq_data = [
        ["Torque / Moment", "M = F × d⊥", "F = applied force; d⊥ = perpendicular moment arm"],
        ["Muscle Force",    "F_m = (W × d_ext) / d_m",
         "d_ext = external moment arm; d_m = muscle moment arm"],
        ["Eccentric Work",  "W_ecc = ∫ F·dθ (negative)",
         "Energy absorbed; muscle lengthens under load"],
        ["GRF Impulse",     "J = ∫ GRF·dt",
         "Area under force-time curve; equals change in momentum"],
        ["Newton's 3rd",    "F_seat = −F_body",
         "Seat reaction force equals body weight at full sit"],
    ]
    eqt = Table(eq_data, colWidths=[3.5*cm, 4.5*cm, 8.0*cm])
    eqt.setStyle(TableStyle([
        ('BACKGROUND',   (0,0), (-1,0), colors.HexColor('#8E44AD')),
        ('TEXTCOLOR',    (0,0), (-1,0), colors.white),
        ('FONTNAME',     (0,0), (1,-1), 'Courier-Bold'),
        ('FONTNAME',     (0,0), (0,-1), 'Helvetica-Bold'),
        ('FONTSIZE',     (0,0), (-1,-1), 7.5),
        ('ALIGN',        (0,0), (-1,-1), 'LEFT'),
        ('VALIGN',       (0,0), (-1,-1), 'MIDDLE'),
        ('ROWBACKGROUNDS',(0,0),(-1,-1),
         [colors.HexColor('#F4ECF7'), colors.HexColor('#FDFEFE')]),
        ('GRID',         (0,0), (-1,-1), 0.5, colors.HexColor('#BDC3C7')),
        ('TOPPADDING',   (0,0), (-1,-1), 5),
        ('BOTTOMPADDING',(0,0), (-1,-1), 5),
    ]))
    story.append(eqt)
    story.append(Spacer(1, 0.5*cm))

    # ── FUNCTIONAL SIGNIFICANCE PAGE ──
    story.append(PageBreak())
    story.append(H('h2', "Functional Significance of StandTS Moment Analysis"))
    story.append(HRFlowable(width='100%', thickness=1.5,
                             color=colors.HexColor('#1ABC9C'), spaceAfter=6))

    fs_data = [
        ["Clinical Aspect", "Biomechanical Basis", "Implication"],
        ["Fall Prevention",
         "Eccentric quadriceps weakness → uncontrolled descent",
         "Strengthen knee extensors eccentrically in elderly"],
        ["Chair Height",
         "Higher chair → smaller knee/hip moment arm → less torque demand",
         "Raise chair height in OA / post-surgical rehab"],
        ["Trunk Lean",
         "More forward lean shifts COM; reduces knee extensor moment",
         "Teach forward lean strategy to compensate for quad weakness"],
        ["TKR / THR Rehab",
         "StandTS is benchmark functional task post-surgery",
         "Target eccentric quad control in rehab protocol"],
        ["Osteoarthritis",
         "Altered joint moments due to pain; compensatory strategies",
         "Monitor for lateral trunk shift, reduced descent speed"],
        ["Obesity",
         "↑ body weight → proportionally ↑ all joint moments",
         "Weight management reduces musculoskeletal joint load"],
        ["5XSTS Test",
         "5-times sit-to-stand speed correlates with quad strength",
         "Standardized fall-risk assessment tool"],
        ["Parkinson's",
         "Impaired eccentric control, timing, and COM transfer",
         "Retrain controlled descent; use cueing strategies"],
    ]
    fst = Table(fs_data, colWidths=[4.0*cm, 6.0*cm, 6.0*cm])
    fst.setStyle(TableStyle([
        ('BACKGROUND',   (0,0), (-1,0), colors.HexColor('#1ABC9C')),
        ('TEXTCOLOR',    (0,0), (-1,0), colors.white),
        ('FONTNAME',     (0,0), (-1,0), 'Helvetica-Bold'),
        ('FONTSIZE',     (0,0), (-1,0), 8),
        ('ALIGN',        (0,0), (-1,-1), 'LEFT'),
        ('VALIGN',       (0,0), (-1,-1), 'MIDDLE'),
        ('FONTSIZE',     (0,1), (-1,-1), 7.5),
        ('ROWBACKGROUNDS',(0,1),(-1,-1),
         [colors.HexColor('#E8F8F5'), colors.white]),
        ('GRID',         (0,0), (-1,-1), 0.5, colors.HexColor('#BDC3C7')),
        ('TOPPADDING',   (0,0), (-1,-1), 5),
        ('BOTTOMPADDING',(0,0), (-1,-1), 5),
    ]))
    story.append(fst)

    doc.build(story)
    print(f"PDF saved: {out_path}")


# ─────────────────────────────────────────────
# RUN
# ─────────────────────────────────────────────

if __name__ == "__main__":
    out = os.path.join(OUT_DIR, "StandTS_Moment_Analysis.pdf")
    build_pdf(out)
Running Command

cd /home/daytona/workspace/standts-pdf && python3 generate_standts_pdf.py 2>&1

Running Command

cd /home/daytona/workspace/standts-pdf && sed -i 's/−/-/g' generate_standts_pdf.…

Editing File

~/standts-pdf/generate_standts_pdf.py

Successfully replaced 1 instance(s) of the string in '/home/daytona/workspace/standts-pdf/generate_standts_pdf.py'
Running Command

cd /home/daytona/workspace/standts-pdf && python3 generate_standts_pdf.py 2>&1

Running Command

ls -lh /home/daytona/workspace/standts-pdf/StandTS_Moment_Analysis.pdf

Your PDF is ready (585 KB, A4, 7 pages):

StandTS Moment Analysis

PDF Document · PDF


What's inside the PDF:
PageContent
Page 1Title page + 4-phase side-by-side overview figure + phase summary table
Pages 2-5One full page per phase - large annotated stick figure with: joint dots (red), GRF arrow (orange), net moment arcs (green), COM star (blue), eccentric muscle labels (purple), joint angle callouts, plus kinetics/kinematics/muscle action data tables
Page 6Joint moment bar chart across all 4 phases (knee vs hip vs ankle), moment analysis summary table, and key biomechanical equations (Torque, Muscle Force, Eccentric Work, GRF Impulse, Newton's 3rd)
Page 7Functional significance table covering falls, chair height, OA, TKR rehab, obesity, Parkinson's, and the 5XSTS test
Each stick figure shows the anatomically correct posture for that phase, with the chair rendered alongside for spatial reference.

assignment on moment analysis for biomechanics .....write task...phases...joints involved....muscles involved....plane and axis....kinetics....kinematics....functional significance right give me subtopics properly ............ in pointers and tabular form .......for .Stair Climbing

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stair climbing biomechanics moment analysis phases joints muscles kinematics kinetics plane axis

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stair ascent descent phases weight acceptance pull-up forward continuance joint moments muscles functional significance

Excellent sources gathered. Here is the full structured assignment:

MOMENT ANALYSIS IN BIOMECHANICS

Movement: STAIR CLIMBING (Stair Ascent)


1. TASK DEFINITION

  • Stair climbing (stair ascent) is the act of propelling the body upward from one step to the next against gravity using the lower extremities.
  • It is a closed-kinetic chain, concentric-dominant movement - muscles shorten to lift the body's mass upward (unlike Stand-to-Sit which is eccentric).
  • It demands significantly higher joint moments than level walking, particularly at the knee (~2x greater than walking).
  • The task requires simultaneous control of forward progression, vertical lift, and lateral stability.
  • It is a cyclic, alternating-limb activity with brief periods of double support at each step transition.
  • Clinically, stair climbing is used as a benchmark of lower limb functional capacity in orthopedic and neurological rehabilitation.
  • Note: Stair descent is the reverse - eccentric-dominant and covered separately in the phase comparison below.

2. PHASES OF STAIR CLIMBING

STAIR ASCENT - Phase Breakdown (McFadyen & Winter Model)

PhaseNameSub-typeEvent MarkersDescription
Phase 1Weight Acceptance (WA)StanceIpsilateral foot-strike → contralateral toe-offLeading foot contacts step; body weight transferred onto stance limb; shock absorption
Phase 2Pull-Up (PU)StanceContralateral toe-off → midpoint of single limb supportKnee extensors pull body upward; main propulsive phase; peak knee moment
Phase 3Forward Continuance (FCN)StanceMid-single limb support → contralateral foot-strikeBody moves forward and upward; ankle push-off generated
Phase 4Push-Up (PU2)StanceContralateral foot-strike → ipsilateral toe-offPlantarflexors push off trailing step; ankle dominant
Phase 5Foot Clearance (FCL)SwingToe-off → mid-swingSwing limb lifts to clear the step edge; hip flexion + knee flexion
Phase 6Foot Placement (FP)SwingMid-swing → foot-strike on next stepSwing limb positioned on next step; controlled forward reach

Key Phase Events:

  • Foot-strike = ipsilateral heel/forefoot contacts next step
  • Toe-off = trailing foot leaves lower step
  • Single limb support = entire body weight on one leg mid-step
  • Stance ~60%, Swing ~40% of cycle (similar ratio to level walking)

3. JOINTS INVOLVED

JointPrimary Motion (Ascent)TypeRange of MotionPhase Active
KneeFlexion → ExtensionConcentric extension (pull-up)0° → ~100° (flex) → 0° (ext)WA, PU, FCN
HipFlexion → ExtensionConcentric extension0° → ~60° flex → 0° extWA, PU, FCN
AnkleDorsiflexion → PlantarflexionConcentric plantarflexion0° → ~20° DF → ~20° PFFCN, Push-Up
SubtalarPronation → SupinationShock absorption / propulsionMinorWA, push-off
Hip (frontal plane)Abduction / adduction controlIsometric/concentricMinorAll stance
Lumbar / PelvisAnterior tilt / lateral tiltStabilizationMinorAll stance
MetatarsophalangealExtension (toe dorsiflexion)Passive extension~50-60°Push-off
Secondary joints:
  • Glenohumeral joint - arm swing for balance
  • Cervicothoracic spine - forward trunk lean for propulsion

4. MUSCLES INVOLVED

Primary Muscles (Stair Ascent - Concentric Action)

Muscle GroupSpecific MusclesJoint ControlledAction TypePeak PhaseRole
QuadricepsRectus Femoris, Vastus Lateralis, Vastus Medialis, Vastus IntermediusKneeConcentricWA + Pull-UpExtend knee to lift body; DOMINANT in stair ascent
Gluteus MaximusGluteus MaximusHipConcentricWA + Pull-UpExtend hip against gravity; major power generator
PlantarflexorsSoleus (primary), Gastrocnemius, PlantarisAnkleConcentricFCN + Push-UpPush off trailing step; propel body upward
IliopsoasIliacus, Psoas MajorHipConcentricFCL (swing)Flex hip to lift swing limb to next step
Hip FlexorsRectus Femoris (bi-articular), TFLHip + KneeConcentricFCLLift thigh for foot clearance
Tibialis AnteriorTibialis AnteriorAnkleConcentric (then eccentric)FPDorsiflexion to clear step; foot placement control

Stabilizing / Secondary Muscles

MuscleJointRolePhase
Gluteus MediusHipFrontal plane pelvic stability; prevents TrendelenburgAll stance
Gluteus MinimusHipHip abductor assistanceStance
HamstringsHip + KneeCo-contraction knee stability; decelerate swingFP, WA
GastrocnemiusKnee + AnkleBi-articular stabilizer; assists push-offFCN
Erector Spinae / MultifidusLumbarTrunk erect during forward leanAll
Adductor MagnusHipHip extensor assist in deeper hip flexion anglesPU
Piriformis / Deep 6 rotatorsHipRotational stability of hipStance
Peroneus Longus / BrevisSubtalarLateral ankle stabilityWA, push-off

5. PLANE AND AXIS OF MOTION

JointPrimary PlaneAxis of RotationPrimary MotionSecondary Planes
KneeSagittalFrontal (mediolateral)Flexion-ExtensionMinor transverse (rotation at full flex)
HipSagittalFrontal (mediolateral)Flexion-ExtensionFrontal (abduction - Glut Med); Transverse (rotation)
AnkleSagittalFrontal (mediolateral)DF - PlantarflexionSubtalar: frontal plane (inversion/eversion)
PelvisFrontal + SagittalA-P axis (lateral tilt); ML axis (anterior tilt)Pelvic tilt + lateral tiltMinor transverse rotation
Hip (frontal)FrontalAnteroposterior axisAbduction (Glut Med)-
TrunkSagittalFrontal (mediolateral)Forward lean (flexion)Minor rotation
Summary:
  • Dominant plane: Sagittal (flexion-extension at all major joints)
  • Dominant axis: Frontal (mediolateral) axis at knee, hip, ankle
  • Secondary plane: Frontal for hip abduction stability (gluteus medius)
  • Tertiary plane: Transverse for minor hip rotation during step-over

6. KINEMATICS

Joint Angular Displacement (Stair Ascent, per cycle)

JointAt Foot-StrikePeak FlexionAt Toe-OffNet Excursion
Knee~20-30° flexion~90-100° flexion (at step-on)~5° flexion~70-80°
Hip~30-40° flexion~55-65° flexion~10-15° extension~70-75°
Ankle~5° dorsiflexion (forefoot contact)~25° dorsiflexion~20° plantarflexion~45° total
PelvisSlight anterior tiltMax anterior tilt at high stepReturns to neutral~10-15°
Trunk~10-15° forward leanMax lean at leading step contactUpright at double support~15-20°

Key Kinematic Points:

  • Forefoot contact is common on stairs (not heel-strike as in level walking) due to step height
  • Higher steps = greater knee and hip flexion angles required at foot placement
  • COM rises approximately equal to step height per step (~15-20 cm standard stair)
  • COM trajectory follows a smooth upward arc, not the oscillating pattern of level walking
  • Step frequency ~85-100 steps/min (slower than level walking cadence)
  • Trunk leans forward more than level walking to aid propulsion and balance

Angular Velocity (Approximate)

JointPeak Angular VelocityPhase
Knee (extension)~120-160°/secPull-Up
Hip (extension)~100-140°/secPull-Up
Ankle (plantarflexion)~150-200°/secPush-Up / FCN

7. KINETICS

Ground Reaction Forces (GRF)

PhaseVertical GRFA-P GRFNotes
Weight Acceptance~100-120% BW (spike)Braking (posterior)Impact absorption on step contact
Pull-Up~110-130% BWPropulsive (anterior)Body being lifted; peak vertical GRF
Forward Continuance~90-100% BWPropulsiveAnkle push-off building
Push-Up~80-90% BWPropulsive (peak)Plantarflexor push-off dominant
Double SupportLoad transitionsTransitionalBrief overlap between limbs

Net Joint Moments (Stair Ascent)

JointMoment TypeDirectionPeak ValuePhaseCompared to Walking
KneeExtension momentExtensor~1.2–1.6 Nm/kgPull-Up~2x greater than level walking
HipExtension momentExtensor~0.8–1.2 Nm/kgWA + Pull-Up~1.5x greater than walking
AnklePlantarflexion momentPlantarflexor~1.3–1.8 Nm/kgFCN + Push-UpSimilar to or slightly greater than walking
Hip (frontal)Abduction momentAbductor (Glut Med)~0.5–0.7 Nm/kgAll stanceGreater than walking

Joint Power (W/kg)

JointPeak PowerTypePhaseSignificance
Knee+3–5 W/kgPositive (concentric)Pull-UpMajor energy generator for lifting body
Hip+2–4 W/kgPositive (concentric)Pull-UpSecond major power generator
Ankle+3–5 W/kgPositive (concentric)Push-Up / FCNPropels body forward and upward
Knee-1 to -2 W/kgNegative (eccentric)WAShock absorption at step contact

8. MOMENT ANALYSIS (Core)

Definition of Moment in Stair Climbing

  • Moment (Torque) = Force × Perpendicular Moment Arm (M = F × d⊥)
  • During ascent, the body's weight creates external flexion moments at hip, knee, and ankle
  • Muscles generate internal extension/plantarflexion moments to overcome gravity (concentric)
  • This is the key difference from StandTS: work is positive (energy generated, not absorbed)

External vs Internal Moment Analysis

JointExternal Moment (Gravity)Internal Moment (Muscle)Net Mechanical WorkDominant Muscle
KneeFlexion (gravity flexes loaded knee)Extension (Quadriceps concentric)PositiveVastus Lateralis / Medialis
HipFlexion (trunk weight over bent hip)Extension (Glut Max concentric)PositiveGluteus Maximus
AnkleDorsiflexion (tibia leans forward over step)Plantarflexion (Soleus concentric)PositiveSoleus (primary)
Hip (frontal)Adduction moment (body weight medial)Abduction (Glut Med concentric)StabilizingGluteus Medius

Moment Arm Considerations

JointMoment Arm Change vs WalkingEffect on Muscle Force Required
KneeLarger (greater flexion angle on step)Requires MUCH greater quadriceps force
HipLarger (deeper hip flexion angle)Requires greater gluteal force
AnkleModerate increaseRequires greater soleus force

Free Body Diagram Concept (Knee, Pull-Up Phase):

  • Body weight (W) acts downward through COM
  • With knee at 80-100° flexion, moment arm (d) is at its largest
  • External knee flexion moment = W × d (maximized at this angle)
  • Quadriceps force (F_q) × patellar tendon moment arm (d_q) must balance it
  • Since d_q is small (~4-5 cm), F_q is 3-5× body weight
  • This explains why stair climbing is more demanding than level walking

9. STAIR ASCENT vs STAIR DESCENT - Comparison Table

ParameterStair AscentStair Descent
Muscle ActionPredominantly concentricPredominantly eccentric
Primary DemandGenerating energy (lift body)Absorbing energy (control lowering)
Peak Knee Moment~1.2-1.6 Nm/kg (extension)~1.5-2.0 Nm/kg (extension - even higher)
Peak Ankle Moment~1.3-1.8 Nm/kg (PF)Lower (DF moment)
GRF~110-130% BW~100-120% BW
Fall RiskLowerHigher (eccentric control failure = fall)
Dominant MuscleQuadriceps (concentric)Quadriceps (eccentric)
PhasesWA, Pull-Up, FCN, Push-Up, FCL, FPWA, FCN, Controlled Lowering, LP, FP
Knee Joint LoadHighHighest (clinically relevant in OA/TKR)

10. FUNCTIONAL SIGNIFICANCE

AspectBiomechanical BasisClinical / Practical Implication
Quadriceps StrengthKnee extensors generate peak moment (~1.2-1.6 Nm/kg) during pull-up; failure = inability to climbStrengthen quads in rehabilitation; stair climbing test = functional strength benchmark
Ankle Push-Off PowerSoleus/gastroc generate 3-5 W/kg to propel body upwardAssess plantarflexor power in elderly and stroke patients; ankle weakness limits stair speed
Hip Extensor ContributionGlut Max generates 2-4 W/kg; compensates if quads are weak via forward trunk leanGlut Max strengthening complements quad rehab
Fall Risk on StairsStair descent is highest-risk ADL for falls; eccentric control failure at kneeTarget eccentric quad training in fall prevention programs
Knee OAStair ascent/descent produces the highest knee joint loads in daily activities (~5-7× BW)Handrail use reduces knee load by 20-30%; step modification; knee OA grading
Step HeightGreater step height → greater knee/hip flexion → larger moment arms → greater muscle force neededReduce step height in elderly housing; rehab starts with lower steps
TKR / THR Post-opStair climbing is the most demanding functional benchmark post-joint replacementCleared for stairs only when adequate quad/glut strength restored (typically 6-12 weeks)
Stroke RehabilitationHemiplegia impairs push-off power and hip flexion for foot clearance → high fall riskStair training with rails; NMES for quad activation; symmetry training
Parkinson's DiseaseReduced step height clearance → step catching → fallsCueing strategies; visual guides on stairs; freezing-of-gait management
ObesityHigher body weight → proportionally higher joint moments and articular cartilage loadsStair avoidance in morbid obesity until weight reduction; physiotherapy planning
Handrail UseTransfers partial load to upper limb; reduces knee moment by ~20%Handrails mandatory in elderly homes; teach correct use
ProstheticsAmputees require above-normal hip power to compensate for absent ankle push-offMicroprocessor prosthetic knees mimic eccentric control on descent

11. QUICK REFERENCE SUMMARY TABLE

ParameterDetails
MovementStair Climbing (Stair Ascent)
Phases (Stance)Weight Acceptance → Pull-Up → Forward Continuance → Push-Up
Phases (Swing)Foot Clearance → Foot Placement
Primary JointsKnee, Hip, Ankle (sagittal plane dominant)
Primary PlaneSagittal
Primary AxisFrontal (Mediolateral)
Secondary PlaneFrontal (hip abduction stability)
Primary MusclesQuadriceps (dominant), Gluteus Maximus, Soleus/Gastroc, Iliopsoas (swing), Gluteus Medius
Muscle Action TypeConcentric (ascent); Eccentric (descent)
Peak Knee Moment~1.2–1.6 Nm/kg (Pull-Up phase)
Peak Ankle Moment~1.3–1.8 Nm/kg (Push-Up / FCN)
Peak Hip Moment~0.8–1.2 Nm/kg (Pull-Up)
Joint PowerKnee + Hip + Ankle all generate positive power (~3-5 W/kg each)
GRF~110-130% BW during pull-up phase
COMRises ~step height per step; smooth upward arc
vs Level Walking1.5-2× greater joint moments; more concentric muscle demand
Functional SignificanceFall prevention, OA/TKR rehab, functional independence, prosthetics

12. APPLIED CLINICAL NOTES

  • Inverse Dynamics calculates net joint moments from motion capture + force plate on instrumented stairs
  • EMG confirms: Vastus Lateralis most active in pull-up; Soleus most active in push-up/FCN
  • Moment normalization to body weight (Nm/kg) allows comparison across subjects
  • Power analysis: All three joints (knee, hip, ankle) show positive power in ascent = triple contributors to lifting body mass
  • Stair Climbing Test (SCT): Time to climb 60 steps correlates with lower limb muscle power in elderly
  • Chair Height equivalence: A 15 cm stair creates similar knee moments to a very low chair sit-to-stand
  • Patellofemoral Joint: During stair ascent at ~60° knee flexion, PFJ reaction force reaches 5-7× body weight - highest of any common daily activity
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