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

Equilibrium Torque 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 Three conditions for equilibrium: 1. Fv = 0 2. Fh = 0 3. T = 0

Equations of 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 Body Center 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