Dynamics I: forces and moments

Dynamics I: Forces and Moments

1. Introduction

Dynamics is the study of motion and the forces that cause it. It is essential in biomechanics, engineering, sports science, and rehabilitation. This topic focuses on two key components:

• Forces: Push or pull that causes acceleration or deformation.

• Moments (Torques): The rotational effect of a force around an axis or point.

Understanding forces and moments helps in analyzing human movement, injury mechanisms, prosthetics, orthopedics, and sports performance.

2. Forces in Biomechanics

a. Types of Forces

Force Type	Description	Example in Human Motion
External Forces	Forces applied from the environment	Ground reaction force during running
Internal Forces	Forces generated within the body	Muscle forces acting on bones
Gravitational Force	Force due to Earth's gravity	Body weight pulling downward
Frictional Force	Resistance between surfaces in contact	Shoe-ground interaction while walking
Joint Reaction Force	Force at the joint due to muscle and external loads	Hip joint reaction force during walking

b. Newton’s Laws of Motion in Biomechanics

1. First Law (Inertia): A body remains at rest or in uniform motion unless acted upon by an external force (e.g., a runner continues moving unless stopped by friction or muscle braking).

2. Second Law (F = ma): Force equals mass times acceleration (e.g., greater muscle force leads to faster sprinting).

3. Third Law (Action-Reaction): Every action has an equal and opposite reaction (e.g., when a person jumps, the ground exerts an equal upward force).

3. Moments (Torques) in Biomechanics

a. Definition of Moment (Torque)

• A moment (torque) is the rotational effect of a force about a pivot point or joint.

• Moment (M) = Force (F) × Perpendicular Distance (d) from the axis of rotation.

b. Examples in Human Motion

• Knee Extension: Quadriceps generate torque to extend the leg.

• Elbow Flexion: Biceps apply force at a distance from the elbow, producing a moment.

• Ankle Plantarflexion: Calf muscles generate torque to push off the ground in running.

c. Moment Arm and Leverage

• Longer moment arms require less force to produce the same torque (e.g., a wrench).

• In biomechanics, lever systems determine the efficiency of movement.

Lever Type	Example in the Human Body	Advantage
First-Class (Fulcrum between Force & Load)	Neck muscles balancing head	Stability & control
Second-Class (Load between Force & Fulcrum)	Standing on toes (calf muscles)	Strong force advantage
Third-Class (Force between Load & Fulcrum)	Biceps lifting forearm	Speed & range of motion

4. Free Body Diagrams (FBDs) in Biomechanics

• FBDs visually represent forces and moments acting on the body.

• Used in gait analysis, prosthetics, and sports science.

Example: Forces in the Knee Joint During Walking

• External forces: Ground reaction force, body weight.

• Internal forces: Muscle tension, ligament forces.

• Moments: Generated by quadriceps, hamstrings, and ground reaction forces.

5. Applications of Forces and Moments in Biomechanics

Field	Application
Sports Science	Optimizing force production for performance (e.g., sprinting, weightlifting)
Injury Prevention	Analyzing excessive forces leading to injuries (e.g., ACL tears)
Rehabilitation	Designing exercises to restore strength and stability
Prosthetics & Orthotics	Engineering devices that replicate natural forces and torques
Ergonomics	Designing workspaces to minimize stress on joints

6. Conclusion

Forces and moments are fundamental to understanding human movement, injury mechanisms, and performance enhancement. By applying principles from dynamics, biomechanics can improve rehabilitation, optimize athletic training, and enhance prosthetic design, ensuring efficient and injury-free movement.