Chapter 13: Equilibrium and

Human Movement

Basic Biomechanics, 4th edition

Susan J. Hall

Presentation Created by

TK Koesterer, Ph.D., ATC

Humboldt State University

Objectives• Define torque, quantify resultant torques, and identify

the factors that affect resultant joint torques• Identify the mechanical advantages associated with the

different classes of levers and explain the concept of leverage within the human body

• Solve basic quantitative problems using the equations of static equilibrium

• Define center of gravity and explain the significance of center of gravity location in the human body

• Explain how mechanical factors affect the body/s stability

EquilibriumTorque

Torque:

• T = Fd

Moment arm:• In the body, moment arm of muscle is the

perpendicular distance between muscle's line pull and joint center

• Largest moment arm at an angle of pull ~900

• Vector quantity, magnitude and direction

– Fd & counterclockwise (+) & clockwise (-)

Resultant Joint Torques

• Product of muscle tension and muscle moment arm produces a torque at the joint crossed by the muscle

• Agonist and antagonist muscle groups• Net joint torque• Concentric and eccentric• Two joint muscles• Factors that affect net joint torques• Speed’s affect on net joint torques

Levers

Lever:

Fulcrum:

First class lever:

Second class lever:

Third class level:

Most levers within the body are third class

Lever Systems

• Moment arm of applied force > moment arm of resistance

• Resistance arm is longer than force arm

Mechanical advantage = Moment arm (force)

Moment arm (resistance)

Anatomical Levers

• In the human body, most lever systems are third class

• Arrangement promotes– Range of motion– Angular speed

• Forces generated must be in excess of the resistance force

• Two components of muscular force– rotary and parallel component

Equations of Static Equilibrium

Equilibrium:• Three conditions for equilibrium:

1. Fv = 0 2. Fh = 0 3. T = 0

Equations of Dynamic Equilibrium

Dynamic equilibrium: Fx - māx = 0

Fy - māy = 0

TG - ī = 0

Center of Gravity (CG)Center of Mass

Center of Mass / Center of Gravity:• The CG of a symmetrical object of

homogeneous density, is the exact center of the object

• When mass in is not constant, CG shifts in the direction of greater mass.

Locating the Center of Gravity

• For one-segment, balance point in three different planes

• As projectile, the body’s CG follows a parabolic trajectory

• Weight vector acts as the CG

Locating the Human BodyCenter of Gravity

Reaction board:• requires a scale, a platform & rigid board with

sharp supports on either end.

Segmental method:• uses data for average locations of individual

body segments CGs as related to a percentage of segment length

Stability and Balance

Stability:• Factors that affect:

– Mass, friction, center of gravity & base of support

Balance:• Foot position affects standing balance

Summary

• A muscle develops tension and produces torque at the joint that it crosses.

• Muscle and bones function as levers.• The angle of muscle pull on a bone produces rotary

and parallel components of force• When a body is motionless, it is in static equilibrium.• The behavior of a body is greatly influenced by

location of center of gravity.• Stability is resistance to disruption og equilibrium