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Link Segment Model. Joint Reaction Forces Muscle Moments Joint Power. Newton’s Laws of Motion. Law of Inertia: A body at rest stays at rest and a body in motion stays in motion unless acted upon by a force or torque.

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Link Segment Model

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Link Segment Model

Joint Reaction Forces

Muscle Moments

Joint Power


Newton’s Laws of Motion

  • Law of Inertia: A body at rest stays at rest and a body in motion stays in motion unless acted upon by a force or torque.

  • Law of Acceleration: The acceleration a body experiences is directly proportional to the force or torque, inversely proportional to the mass or moment of inertia and occurs in the direction of the force or torque.

  • Law of Reaction: For every action there is an opposite reaction.


Newton’s First Law: Law of Inertia

Law of Inertia: A body at rest stays at rest and a body in motion stays in motion unless acted upon by a force or torque.

Mass is the measure of an object’s resistance to linear change.

Moment of inertia is the measure of an object’s resistance to angular change.

ΣF = m a ΣT = Iα

To solve for forces and torques, we need both mass and moment of inertia.


Moment of Inertia (I)

ICG= 3.5 kg·m2

  • The Moment of Inertia (I) represents an objects resistance to angular change about some axis.

  • Moment of inertia is a sum of the product of mass times the squared distance of the mass about the axis.

  • When body parts are moved closer to the axis of rotation the moment of inertia (resistance to spin) is reduced.

ICG= 15 kg·m2

ICG= 6.5 kg·m2

ICG= 83 kg·m2


Link Segment Model Assumptions

  • Each segment has a fixed mass located at its center of mass

  • The joints are considered as hinge joints

  • The moment of inertia is fixed during movement

  • The length of each segment is constant


Input Information to Solve for Joint Forces and Torques

  • Mass & moment of inertia of each segment.

  • Location of each segments Center of Mass (CM).

  • Position, velocity, acceleration of each segments CM (x, y, Vx, Vy, Ax, Ay).

  • Angular position, velocity, acceleration about each segments CM (Θ, ω, α).

  • External forces for all contact points.

  • Center of pressure or location of external forces acting on the body.

Center of Pressure gives the location of external forces acting on the body.


Inverse Dynamics: Finding Forces & Torques from Position Data. [working backward to solve for forces & torques]


Anatomical Relationship


Forces & Torques Acting On Each Segment


Joint Moments


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