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Chapter 13: Equilibrium and Human Movement

Chapter 13: Equilibrium and Human Movement. Basic Biomechanics, 4 th edition Susan J. Hall. Objectives. Define torque, quantify resultant torques, and identify the factors that affect resultant joint torques

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Chapter 13: Equilibrium and Human Movement

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  1. Chapter 13: Equilibrium andHuman Movement Basic Biomechanics, 4th edition Susan J. Hall

  2. 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

  3. EquilibriumTorque Torque: the rotary effect of a force about an axis • Aka Moment of Force • Torque is product of force and force’s moment arm • T = Fd

  4. EquilibriumTorque • T = Fd Moment arm: the perpendicular distance from force’s line of action to axis of rotation Moment arm sometimes referred to as force arm A force directed through axis of rotation (centric) causes no rotation.

  5. EquilibriumTorque • In the body, moment arm of muscle is the perpendicular distance between muscle's line of pull and joint center • Largest moment arm at an angle of pull ~900

  6. EquilibriumTorque When is the moment arm the greatest?

  7. EquilibriumTorque • Force couple is two equal and opposite parallel eccentric forces exerted simultaneously on opposite sides of the axis of rotation. • Torque generated by a couple is sum of products of each force and its moment arm.

  8. EquilibriumTorque • Torque (Fd ) is a vector quantity, has magnitude and direction • counterclockwise (+) & clockwise (-)

  9. Resultant Joint Torques • Product of muscle tension and muscle moment arm produces a torque at the joint crossed by the muscle • Sum of 3 elbow flexor torques • Antagonist create torque in opposite direction. • Mvmt depends on net torque.

  10. Resultant Joint Torques • Tension in antagonist controls velocity & enhances joint stability. • Concentric: when muscle torque & joint movement in same direction. • Eccentric: when muscle torque & joint movement opposite.

  11. Resultant Joint Torques • Concentric and eccentric complicated in two joint muscles • Two joint muscles • Concentric at one joint • Eccentric at a second joint • Can you give an example? • 3 factors that affect net joint torques: segment weight, motion of segment, external forces • How does speed affect net joint torques?

  12. Levers Lever: a rigid barlike body that rotates about an axis Fulcrum:the point of support, or axis of rotation First class lever:Force – Axis - Resistance Second class lever: Axis – Resistance - Force Third class level:Axis – Force - Resistance Most levers within the body are third class

  13. First Class Levers

  14. Key Term • First-class lever: A lever for which the muscle force and resistive force act on opposite sides of the fulcrum.

  15. Figure 4.3 • O = fulcrum; FM = muscle force; FR = resistive force; MM = moment arm of the muscle force; MR = moment arm of the resistive force. • Mechanical advantage = MM /MR = 5 cm/40 cm = 0.125, which, being less than 1.0, is a disadvantage. • The depiction is of a first-class lever because muscle force and resistive force act on opposite sides of the fulcrum.

  16. Second Class Levers

  17. Key Term • Second-class lever: A lever for which the muscle force and resistive force act on the same side of the fulcrum, with the muscle force acting through a moment arm longer than that through which the resistive force acts. • Due to its mechanical advantage, the required muscle force is smaller than the resistive force.

  18. Figure 4.4 • The slide shows plantar flexion against resistance (e.g., a standing heel raise exercise). • FM = muscle force; FR = resistive force; MM = moment arm of the muscle force; MR = moment arm of the resistive force. • When the body is raised, the ball of the foot, the point about which the foot rotates, is the fulcrum (O). • Because MM is greater than MR, FM is less than FR.

  19. Third Class Levers

  20. Key Term • Third-class lever: A lever for which the muscle force and resistive force act on the same side of the fulcrum, with the muscle force acting through a moment arm shorter than that through which the resistive force acts. • The mechanical advantage is thus less than 1.0, so the muscle force has to be greater than the resistive force to produce torque equal to that produced by the resistive force.

  21. Figure 4.5 • The slide shows elbow flexion against resistance (e.g., a biceps curl exercise). • FM = muscle force; FR = resistive force; MM = moment arm of the muscle force; MR = momentarm of the resistive force. • Because MM is much smaller than MR, FM must be much greater than FR.

  22. Functions of Levers Machines function in four ways: • To balance multiple forces. • To enhance force in attempt to reduce the total force needed to overcome a resistance. • To enhance range of motion and speed of movement so that a resistance may be moved farther or faster. • To alter the resulting direction of the applied force. R. T. Floyd, Manual of Structural Kinesiology.

  23. Functions of Levers Lever system can serve one of two purposes • If moment arm of applied force > moment arm of resistance, force magnified. • If resistance arm > force arm, range of motion magnified. Susan J. Hall. Basic Biomechanics. Mechanical advantage = Moment arm (force) Moment arm (resistance)

  24. Anatomical Levers • In the human body, most lever systems are third class (MA<1). • Arrangement promotes • Range of motion • Angular speed • Forces generated must be in excess of the resistance force

  25. Analysis of Anatomical Levers • Force of muscle group represented by Force Vector (Fm). • The Angle of Pull of muscle is angle Fm makes with longitudinal axis of bone to which it attaches (axis side). • Force Vector (Fm) can be resolved into two perpendicular components. Figure 6-20

  26. Analysis of Anatomical Levers • Two components of muscular force (Fm ) • Rotary: part of Fm that acts to rotate the lever. • Parallel: part of Fm directed parallel to bone. • Stabilizing: parallel component directed toward joint center. • Dislocating: parallel component directed away from joint center. Figure 6-21

  27. Analysis of Anatomical Levers • As Force Vector (Fm) approaches 90 to longitudinal axis of bone, its rotary component becomes larger & dislocating or stabilizing becomes smaller. • When angle is 90 to bone, the rotary force is 100% of muscular force. Figure 13-14

  28. Equations of Static EquilibriumPrinciple of Levers Static Equilibrium: • Three conditions for static equilibrium: • Fv = 0, sum of vertical forces • Fh = 0, sum of horizontal forces • T = 0, sum of torques So, torques on one side (+) = torques on other (-) Force (+) x moment arm = Force (-) x moment arm

  29. Principle of Levers Force x Force Arm = Resistance x Resistance Arm

  30. Static Equilibrium • Second Class Lever mechanical advantage is always > 1 because FA > RA. • Push up is a second class lever. • If you have a long torso, short legs, A, B or C? • If you have long legs, short torso, A, B or C?

  31. Static Equilibrium • Third class lever mechanical advantage always < 1 because FA always < RA. • Leg extension is a third class lever • If you have long legs are you A, B, or C? • If you have short legs are you A, B or C?

  32. Equations of Dynamic Equilibrium Bodies in motion considered to be in state of dynamic equilibrium. Dynamic equilibrium: concept indicating a balance between applied forces and inertial forces of a body in motion. • Fx - māx = 0 • Fy - māy = 0 • TG - ī = 0 D’Alembert’s principle: “elevator experience”

  33. Dynamic Equilibrium • As elevator accelerates upward, inertial force in opposite direction created by BW force on plate increases. • As elevator accelerates downward, inertial force decreases BW on plate. • Body weight remains constant, inertia varies reaction force.

  34. Center of Gravity (CG)Center of Mass Center of Mass / Center of Gravity: a unique point around which body’s mass equally distributed in all directions. • The CG of a symmetrical object of homogeneous density, is the exact center of the object • When mass distribution in object is not constant, CG shifts in the direction of greater mass.

  35. Center of Gravity • For one-segment object, balance point in 3 different planes • A body behaves as though all mass concentrated at the CG. • As a projectile, the body’s CG follows a parabolic trajectory, regardless of changes of body segment configuration.

  36. Center of Gravity • Path of CG may be an index of performance proficiency in several sports.

  37. Locating the Human BodyCenter of Gravity Locating the CG for a body containing two or more moveable, interconnected segments more difficult than for non-segmented. Reaction board: • requires a scale, a platform & rigid board with sharp supports on either end.

  38. Locating the Human BodyCenter of Gravity Appendix D. Hall, p. 527. Segmental method: • uses data for average locations of individual body segments CGs as related to a percentage of segment length

  39. Stability and Balance Balance: the ability to control equilibrium, static or dynamic. To achieve balance, hence equilibrium, need to maximize stability.

  40. Stability and Balance Stability: resistance to a change in the body’s acceleration; resistance to disturbance in body’s equilibrium (static or dynamic). • Examples when stability desirable? • Examples when minimum stability desired?

  41. Stability and Balance Factors that affect balance • Mass: greater mass greater balance • Friction • Height of center of gravity: lower greater balance • Base of support: larger greater balance • Base of support related to CG

  42. 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 of equilibrium

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