Link Segment ModelLink Segment Model

Joint Reaction ForcesJoint Reaction Forces

Muscle MomentsMuscle Moments

Joint PowerJoint Power

Newton’s Laws of MotionNewton’s Laws of Motion

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

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

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

Newton’s First Law: Law of InertiaNewton’s First Law: Law of Inertia

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

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

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

ΣΣF = m a F = m a ΣΣT = IT = Iαα

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

Moment of Inertia (I)Moment of Inertia (I)

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

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

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

ICG= 3.5 kg·m2

ICG= 6.5 kg·m2ICG= 15 kg·m2

ICG= 83 kg·m2

2CGI md

Link Segment Model AssumptionsLink Segment Model Assumptions

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

The joints are considered as hinge jointsThe joints are considered as hinge joints The moment of inertia is fixed during movementThe moment of inertia is fixed during movement The length of each segment is constantThe length of each segment is constant

Input Information to Input Information to Solve for Joint Forces Solve for Joint Forces

and Torquesand Torques

Mass & moment of inertia of Mass & moment of inertia of each segment.each segment.

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

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

Angular position, velocity, Angular position, velocity, acceleration about each acceleration about each segments CM (segments CM (ΘΘ, , ωω, , αα).).

External forces for all contact External forces for all contact points.points.

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

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

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

Anatomical RelationshipAnatomical Relationship

Forces & Torques Acting On Each SegmentForces & Torques Acting On Each Segment

Joint MomentsJoint Moments