Chapter 13

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Chapter 13: Equilibrium and Human Movement: 

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: 

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: 

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 effect 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 a simple machine consisting of a relatively rigid bar-like body that may be made to rotate about an axis


Fulcrum the point of support, or axis, about which a lever may be made to rotate

First Class Lever: 

First Class Lever lever positioned with the applied force and the resistance on opposite sides of the axis of rotation

Second Class Lever: 

Second Class Lever lever positioned with the resistance between the applied force and the fulcrum

Third Class Lever: 

Third Class Lever lever positioned with the applied force between the fulcrum and resistance





Lever Systems: 

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: 

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







Factors Affecting Muscular Force Generation: 

Factors Affecting Muscular Force Generation Force-Velocity Relationship Length-Tension Relationship Electromechanical Delay Stretch-Shortening Cycle

Force-Velocity Relationship: 

Force-Velocity Relationship Maximal force developed by muscle governed by velocity of muscle’s shortening or lengthening. Holds true for all muscle types Does not imply: It’s impossible to move heavy resistance at a fast speed. It’s impossible to move light loads at low speeds



Force-Velocity Relationship: 

Force-Velocity Relationship Maximum isometric tension Eccentric conditions Volitionally Represents contribution of the elastic components of muscle Eccentric Strength Training More effective than concentric training in increasing muscle size and strength.

Length-Tension Relationship: 

Length-Tension Relationship In human body, force generation increases when muscle is slightly stretched. Parallel fibers at max just over resting length Pennate fibers at max with 120%-130% resting length. Due to contribution of elastic components of muscle (primarily the SEC)

Electromechanical Delay: 

Electromechanical Delay The time between arrival of neural stimulus and tension development by the muscle Varies among human muscles (20-100 msec) Short EMDs produced by muscles with high percentage of FT fibers Not affected by muscle length, contraction type, contraction velocity, or fatigue

Stretch-Shortening Cycle: 

Stretch-Shortening Cycle Pattern of eccentric contraction followed immediately by concentric contraction Elastic Recoil Stretch Reflex Activation Muscle can perform more work with active stretch prior to shortening contraction Eccentric training increases ability of musculotendinous unit to store and produce more elastic energy.

Muscular Strength, Power, and Endurance: 

Muscular Strength, Power, and Endurance Muscular Strength Muscular Power Muscular Endurance Muscular Fatigue Effect of Muscle Temperature

Muscular Strength: 

Muscular Strength The ability of a given muscle group to generate torque at a particular joint. Derived from: amount of tension the muscles can generate moment arms of contributing muscles with respect to joint center.

Muscular Strength: 

Muscular Strength Tension-generating capability of a muscle affected by: Cross-sectional area Training state Moment arm of a muscle affected by: Distance between the muscle’s anatomical attachment to bone and the axis of rotation at the joint center Angle of muscle’s attachment to bone.

Muscular Power: 

Muscular Power The product of muscular force and the velocity of muscular shortening. The rate of torque production at a joint Max. power occurs at: approx. 1/3 max. velocity, and approx. 1/3 max concentric force Affected by muscular strength and movement speed



Muscular Endurance: 

Muscular Endurance The ability to exert tension over a period of time. Constant: gymnast in iron cross Varying: rowing, running, cycling Length of time dramatically affected by force and speed requirements of activity. Training involves many repetitions with light resistance.

Resistance Devices used in Strength Training: 

Resistance Devices used in Strength Training

Free Weights: 

Free Weights Gravity dependent Resistance pattern constant or variable Concentric & Eccentric action of same muscles Antagonistic muscles not utilized Momentum may be a factor in resistance pattern

Gravity Dependent Machines: 

Gravity Dependent Machines Universal Gym Resistance moves upward Round pulleys changes direction of resistance Constant resistance

Variable Resistance Machines: 

Variable Resistance Machines Nautilus Cam design creates variable resistance Designed to mimic the strength curve

Isokinetic Devices: 

Isokinetic Devices Biodex, Cybex, Orthotron, and hydraulic equipment Accommodating resistance Constant velocity

Other Devices: 

Other Devices The body – pushups, sit-ups, pull-ups Pushup variations Sit-ups, curl-ups - changing resistance Pull-ups – pronated vs. supinated grip

Equations of Static Equilibrium: 

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

Equations of Dynamic Equilibrium: 

Equations of Dynamic Equilibrium Dynamic equilibrium: Fx - māx = 0 Fy - māy = 0 TG - ī = 0

Center of Gravity (CG) Center of Mass: 

Center of Gravity (CG) Center of Mass The point around which the mass and weight of a body are balanced in all directions The CG of a symmetrical object of homogeneous density is the exact center of the object When mass within an object is not constant, CG shifts in the direction of greater mass



Locating the Center of Gravity: 

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 through the CG (line of gravity)



Locating the Human Body Center of Gravity: 

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 and Balance Stability: resistance to disruption of equilibrium Factors that affect stability: Mass, friction, horizontal position and height of center of gravity with respect to the base of support Balance: ability to control equilibrium 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 the location of the center of gravity. Stability is the resistance to disruption of equilibrium


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