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MOMENT ANALYSIS IN BIOMECHANICS

Assignment: Sit-to-Stand (STS) Movement

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TABLE OF CONTENTS

1. Introduction & Definition of Moment of Force
2. Task Description
3. Phases of Sit-to-Stand
4. Joints Involved
5. Muscles Involved
6. Plane and Axis of Movement
7. Kinematics
8. Kinetics and Moment Analysis
9. Functional Significance
10. Clinical Applications
11. Summary Table
12. References

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1. INTRODUCTION

M = F × d⊥

• M = Moment (Newton-metres, Nm)
• F = Applied force (Newtons)
• d⊥ = Perpendicular distance from line of action of force to the joint axis (moment arm, metres)

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2. TASK DESCRIPTION

• Requires the highest muscle demand of any routine ADL
• Peak knee extensor moment during STS approaches maximum voluntary capacity in older adults
• It is a reliable clinical functional test (5-times STS test, 30-second STS test)
• Impairment in STS is an early indicator of functional decline

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3. PHASES OF SIT-TO-STAND

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Phase 1: Flexion Momentum Phase

• The trunk flexes forward (forward lean of approximately 30-40° from vertical)
• Centre of mass (COM) shifts forward over the base of support
• Body weight is still partially transferred through the seat
• Anterior momentum is generated
• Preparatory ankle dorsiflexion begins
• Ends just before seat-off (SO)

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Phase 2: Momentum Transfer Phase

• Buttocks leave the chair - full body weight now transferred to feet
• Horizontal (forward) momentum converts to vertical (upward) momentum
• Hip begins extending; knee is still flexed at ~90°
• Maximum ankle dorsiflexion occurs at the end of this phase
• Ground reaction force rises sharply

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Phase 3: Extension Phase (Rising Phase)

• All three joints extend simultaneously (hip, knee, ankle plantarflexion)
• COM rises vertically
• Lower leg tilts backward (tibia moves to vertical)
• Peak joint moments are generated in this phase
• Most energy-demanding phase of STS

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Phase 4: Stabilization Phase

• Body reaches upright position
• COM settles over the base of support
• Postural muscles activate for balance
• Momentum reduces to zero
• Hip, knee, and ankle approach neutral alignment

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4. JOINTS INVOLVED

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5. MUSCLES INVOLVED

Phase 1 - Flexion Momentum Phase

Phase 2 - Momentum Transfer (Seat-Off)

Phase 3 - Extension Phase

Phase 4 - Stabilization Phase

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6. PLANE AND AXIS OF MOVEMENT

Primary Plane and Axis

Secondary Planes (Minor Contributions)

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7. KINEMATICS

7.1 Joint Angular Kinematics

7.2 Linear Kinematics of Centre of Mass (COM)

• Phase 1: COM moves anteriorly (forward, horizontal displacement ~12-15 cm)
• Phase 2: COM transitions from forward to upward movement
• Phase 3: COM rises vertically (~45-55 cm from seated to standing height)
• Phase 4: COM settles with minimal sway

7.3 Angular Velocity

• Peak angular velocity at the knee occurs during Phase 3 (extension phase)
• Trunk angular velocity peaks early in Phase 1 during forward lean
• Hip angular velocity peaks just after seat-off

7.4 Temporal Data

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8. KINETICS AND MOMENT ANALYSIS

8.1 Ground Reaction Force (GRF) During STS

• Before seat-off: GRF < body weight (chair shares load)
• At seat-off: GRF = body weight (impulsive rise to 100% BW)
• During extension phase: GRF transiently exceeds body weight (vertical impulse to accelerate COM upward)
• At standing: GRF = body weight

8.2 Moment Analysis - Concept

M_ext = GRF × d (perpendicular distance from GRF line of action to knee joint centre)

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8.3 Joint Moment Values During STS

Knee Joint Moment

• Dominant moment: Knee extensor moment
• Generated by: Quadriceps femoris
• Peak value: ~0.45-0.50 Nm/kg (normalized to body weight)
• Critical threshold: Combined hip + knee peak moment must exceed 1.53 Nm/kg for successful STS
• Phase: Peaks during Phase 2-3 (seat-off to maximum dorsiflexion)
• Clinical note: Knee extensor moment during STS approaches maximum voluntary capacity in older adults, explaining why STS is the first ADL to fail with age

Hip Joint Moment

• Dominant moment: Hip extensor moment
• Generated by: Gluteus maximus, hamstrings
• Peak value: ~0.24-1.92 Nm/kg (highly variable, depends on trunk lean strategy)
• Phase: Peaks just after seat-off (Phase 2-3)
• Relationship to knee: If hip moment is reduced (e.g., trunk more upright), knee must compensate, and vice versa - they are complementary (Roebroeck et al., 1994)

Ankle Joint Moment

• Dominant moment: Plantarflexion moment (eccentric in Phase 1, concentric in Phase 3)
• Generated by: Gastrocnemius and soleus
• Peak value: ~0.02-1.32 Nm/kg
• Phase: Dorsiflexion moment in Phase 1 (tibialis anterior); plantarflexion moment in Phase 3

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8.4 The Hip-Knee Trade-Off: A Key Concept in Moment Analysis

M_hip + M_knee ≈ 1.53 Nm/kg (minimum required)

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8.5 Inverse Dynamics Model (for STS Moment Calculation)

1. Measure: GRF using force plate + kinematics using motion capture
2. Input: Segment masses, COM positions, GRF vector
3. Calculate: Starting from the most distal segment (ankle), work proximally:
   • Ankle moment → Knee moment → Hip moment
4. Formula at each joint:

   M_joint = M_external - (I × α) - (m × a × r)

   Where I = moment of inertia, α = angular acceleration, m = segment mass, a = linear acceleration of COM, r = moment arm

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8.6 Summary of Moments by Phase

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9. FUNCTIONAL SIGNIFICANCE

9.1 STS as a Functional Threshold Test

• Combined hip + knee moment < 1.5 Nm/kg indicates need for rehabilitation
• Inability to perform STS without arm support indicates significant lower limb weakness

9.2 Biomechanical Strategies Used by Individuals

• Large forward trunk lean generates anterior momentum
• Reduces quadriceps demand; hip extensors contribute more

• Minimal forward lean, slow deliberate movement
• Higher quadriceps demand; increased fall risk
• Requires more muscle force per unit time

9.3 Relationship to Falls Prevention

• STS difficulty is one of the strongest predictors of falls in older adults
• Reduced knee extensor moment capacity = first functional loss
• Timed STS test (5x STS in seconds) is a validated falls screening tool

9.4 Clinical Relevance of Moment Analysis

9.5 Chair Height and Moment Modification

• Lowering chair height increases both hip and knee extensor moments significantly
• Seat height of 40 cm → peak hip and knee moments are 1.7x greater than at 60 cm seat height (PMC3995647)
• Clinical use: Raising chair height reduces joint demand - recommended for post-surgical patients

9.6 Arm Use During STS

• Using armrests or pushing off knees reduces knee extensor moment by ~30%
• Reduces the functional demand on quadriceps
• Used as a rehabilitation progression tool

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10. CLINICAL APPLICATIONS

1. Rehabilitation planning: Inverse dynamics moment values guide muscle strengthening targets (e.g., quadriceps must produce at least 0.45 Nm/kg for independent STS)
2. Prosthetic and orthotic design: STS moment data informs knee and ankle joint alignment in prostheses and AFOs
3. Ergonomic chair design: Seat height, armrest placement, and seat tilt angle modify moment demands
4. Pre/post-surgical evaluation: STS kinetics assess outcome after TKR, THR, or ACL repair
5. Fall risk screening: 5x STS test and 30-second STS test are standardized, validated measures
6. Geriatric assessment: STS performance predicts hospitalization, nursing home admission, and mortality in older adults

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11. SUMMARY TABLE

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12. REFERENCES

1. Hughes MA, Schenkman ML. Analysis of sit-to-stand movement phases. J Rehabilitation Research Development. 1996.
2. Roebroeck ME et al. Computation of the kinematics and minimum peak joint moments of sit-to-stand movements. BioMedical Engineering Online. 2007. doi:10.1186/1475-925X-6-26
3. Yoshioka S et al. Peak hip and knee joint moments during STS are invariant to seat height within low-normal range. PLoS ONE. 2014. PMC3995647
4. Kinematic analysis of the human body during sit-to-stand in healthy adults. PMC8183776
5. Biomechanical analysis of STS following knee replacement. ISB Congress 2013.

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SUBTOPICS AT A GLANCE (Quick Reference)

1. Introduction
   ├── Definition of moment / torque
   ├── Formula: M = F × d⊥
   └── Why STS is chosen as model task

2. Task Description
   ├── Definition of STS
   ├── Frequency in daily life
   ├── Standardized conditions
   └── Clinical relevance

3. Phases (4 phases by Hughes & Schenkman)
   ├── Phase 1 - Flexion Momentum
   ├── Phase 2 - Momentum Transfer
   ├── Phase 3 - Extension (Rising)
   └── Phase 4 - Stabilization

4. Joints Involved
   ├── Ankle, Knee, Hip (primary)
   └── Lumbar spine, Pelvis (secondary)

5. Muscles Involved
   ├── Phase-wise muscle activity
   ├── Agonists / stabilizers
   └── Concentric vs eccentric roles

6. Plane and Axis
   ├── Sagittal plane - primary
   ├── Mediolateral axis
   └── Minor frontal/transverse contributions

7. Kinematics
   ├── Joint ROM (angle values)
   ├── COM displacement (horizontal & vertical)
   ├── Angular velocity
   └── Temporal parameters

8. Kinetics & Moment Analysis
   ├── GRF changes across phases
   ├── External vs internal moments
   ├── Knee extensor moment (peak ~0.45-0.50 Nm/kg)
   ├── Hip extensor moment (peak ~0.24-1.92 Nm/kg)
   ├── Ankle plantarflexion moment
   ├── Hip-Knee complementary trade-off
   └── Inverse dynamics method

9. Functional Significance
   ├── Threshold for independence
   ├── Momentum vs quasi-static strategies
   ├── Falls risk and STS tests
   └── Effect of chair height and arm use

10. Clinical Applications
    ├── Post-surgical rehab (TKR, THR)
    ├── Stroke, Parkinson's, sarcopenia
    ├── Ergonomic design
    └── Outcome measurement

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