KIN 2241
Torques: turning effect produced by force (moment)
● Proportional to magnitude of force and distance between line
● Motion of restrained system
○ Axis of rotation + one side fixed in space
○ Force applied away from axis
■ Force: magnitude, point of application, direction, and line of axis
○ Moment arm: perpendicular distance between line of action and axis of rotation
■ Moment arm: shortest distance, between axis and line force is
○ Lever arm: point of force application and axis of rotation acting on
● Torque = force x moment arm distance (radius)
○ Direction: counter clockwise = + vs. clockwise = -
● Torque of humans
○ All muscle produce torque
○ Muscle force → net joint torque → motion
■ Concentric: internal moment and motion is same direction (contraction of
muscle)
■ Eccentric: internal moment are motion are in opposite direction (extension
of muscles)
○ Muscle force components
■ Rotatory component: perpendicular to bone, internal moment, cause
motion
■ Non-rotatory component: perpendicular to rotatory, parallel to bone
● No internal moment contribution, joint compression/distraction
○ Stabilization/dislocation
■ Joint position influences magnitude and direction of muscle force
● Change of joint position = change of non-rotary and rotatory
component
○ Impacted by muscle force, angle of pull and lever arm
Muscle Contributions
● Muscles produce co-contractions (opposing joint torques)
○ Motion occurs in direction of net internal moment
○ Antagonist muscle: produce stabilization & control velocity at a joint
● Individuals with ACL ruptures have deficits among all indices
○ Quadricep and hamstring function effected
■ More hamstring = higher stabilization/control/resistance
● However, leads to higher compressive force (bony contact occurs)
○ Greater co-contraction with osteoarthritis and ACL injuries (stiff gait, reduced
knee flexion)
■ Osteoarthritis (OA): knee adduction in OA patients leads to higher
adduction moment in knee and increases medial joint compression
● Joint Torque (non-muscle contributions)
○ Segment mass and external objects
Equilibrium: balanced forces/torques, body motionless
, ● Forces = 0 (horizontal/vertical force and torque
● Statics: angular acceleration = 0 → sum of moments = 0 (moments counterclockwise
and moments clockwise = 0)
● Sum of torques = (Fm) (dm) + (-wt)(dwt)
Levers: consists of a rigid bar (bone) & rotate around a fulcrum (joint)
● Force applied to lever moves resistance (muscle = force)
● Consists of axis of rotation, motive/applied force, resisted force
● First class Lever (MAR)
○ Axis in center, motive on one side, resistance on another
■ Like see-saw, antagonist vs agonist muscle
● Second Class Lever (ARM)
○ Resistance in middle, axis is first, motive at end
■ Push ups: feet are the axis, resistance is the center of mass and the
motive are when the arms push up
● Third Class Lever (AMR)
○ Axis is at one end, motive in the middle, resistance at the end
■ Most joints are like this
● Advantages: good ROM and speed
● Disadvantages: force produced
● Mechanical advantage vs disadvantage ratio
○ Mechanical advantage (MA) = Lever arm motive/lever arm resistance
■ MA < 1: disadvantage
● Muscle force greater than resisted
○ Line of action close to axis = shorter lever arm
■ MA > 1: advantage
● Some 1st class lever and all 2nd class levers
○ Muscle force less than resisted force
○ Farther from axis = higher distance moved = higher
velocity
Angular Motion: rotation around a fixed point, within our outside a body
● Measured in degrees, revolutions: 1 = 360 degrees (qualitative)
● Radians: 1 Rad = 57.3 degrees
○ Arc length/radius, radius is dimensionless
○ π rad = 180 degrees
● Distance: angular change in path of motion → analogous to linear distance
● Displacement: final - initial position (indicates direction)
● Speed vs Velocity
○ (ω) = ΔӨ/t ← velocity
○ (a) = Δω/t ← acceleration
● Linear vs angular relationship: motion of any part of body can be explained in linear
terms
○ Need axis, radius of rotation, and kinematics in radians
○ d = Өr ← use radians for Ө
■ Higher radius of rotation = higher linear displacement
, ○ Vt = ωr ← radians for ω, linear velocity of rotating object is tangential to path of
motion
■ Longer radius = more velocity (longer golf club = more distance)
■ Using full extension, increase radius length = more velocity
○ Linear Tangential velocity: vt = (angular velocity) (radius)
■ Change degrees to rad for angular velocity
○ radial acceleration at the instant prior to the point of release: (ω^2)r or (vt^2)/r
Angular Acceleration: acceleration of a body in angular motion which may be resolved into its
components
● Radial: centripetal (toward center)
○ Object must be forced to follow a curved path
○ Change in direction = change in velocity = acceleration occurs
■ Acceleration to required to keep body in curved path
○ Hammer Throw/Throwing in general
■ Ball follows curved path from restraining force of arm
■ The restraining for causes ar toward center of curved path
● ar = v^2/r ← radial acceleration equation
○ Lower the radius = higher radial acceleration
● Release = 0 ar, ball follows path of tangent center of curved path
○ Banked turns in driving
■ Allows sharper turn without decreasing speed
■ Addition centripetally directed force
○ Directed towards center along curved pathway (representing change in direction)
■ Linear speed of an object traveling a curved path remains constant
■ Direction constantly changes = velocity constantly changes = radial
acceleration occurs
● Caused by GRF directed to center of turn
● Tangential: change in linear for a body traveling curved path
Angular Kinetics: causes of angular motions
● Center of Mass: mass or weight is concentrated
○ Equilibrium: equal torque on each side of fulcrum
○ Index of total body motion: Track center of gravity during motion
■ Either whole body or segments: % body height or %segment length
● Location shows where body respond to external forces
■ Center of gravity (COG) changes as body moves
● Balance Method: weight and vertical reaction force at fulcrum must be in same plane
○ High jump: manipulates center of gravity
■ As they reach higher height, without raising COG, therefore easier to
make jump
● Suspension method: same as balance method, easier to accomplish at fulcrum on top
● MRI Reconstruction: high cost, big and bulky, impractical
○ Reconstructs the the tissues in imaging
● Segmental Method: determine center of gravity for each segment experimentally
○ Center of gravity/segment length = ratio
Torques: turning effect produced by force (moment)
● Proportional to magnitude of force and distance between line
● Motion of restrained system
○ Axis of rotation + one side fixed in space
○ Force applied away from axis
■ Force: magnitude, point of application, direction, and line of axis
○ Moment arm: perpendicular distance between line of action and axis of rotation
■ Moment arm: shortest distance, between axis and line force is
○ Lever arm: point of force application and axis of rotation acting on
● Torque = force x moment arm distance (radius)
○ Direction: counter clockwise = + vs. clockwise = -
● Torque of humans
○ All muscle produce torque
○ Muscle force → net joint torque → motion
■ Concentric: internal moment and motion is same direction (contraction of
muscle)
■ Eccentric: internal moment are motion are in opposite direction (extension
of muscles)
○ Muscle force components
■ Rotatory component: perpendicular to bone, internal moment, cause
motion
■ Non-rotatory component: perpendicular to rotatory, parallel to bone
● No internal moment contribution, joint compression/distraction
○ Stabilization/dislocation
■ Joint position influences magnitude and direction of muscle force
● Change of joint position = change of non-rotary and rotatory
component
○ Impacted by muscle force, angle of pull and lever arm
Muscle Contributions
● Muscles produce co-contractions (opposing joint torques)
○ Motion occurs in direction of net internal moment
○ Antagonist muscle: produce stabilization & control velocity at a joint
● Individuals with ACL ruptures have deficits among all indices
○ Quadricep and hamstring function effected
■ More hamstring = higher stabilization/control/resistance
● However, leads to higher compressive force (bony contact occurs)
○ Greater co-contraction with osteoarthritis and ACL injuries (stiff gait, reduced
knee flexion)
■ Osteoarthritis (OA): knee adduction in OA patients leads to higher
adduction moment in knee and increases medial joint compression
● Joint Torque (non-muscle contributions)
○ Segment mass and external objects
Equilibrium: balanced forces/torques, body motionless
, ● Forces = 0 (horizontal/vertical force and torque
● Statics: angular acceleration = 0 → sum of moments = 0 (moments counterclockwise
and moments clockwise = 0)
● Sum of torques = (Fm) (dm) + (-wt)(dwt)
Levers: consists of a rigid bar (bone) & rotate around a fulcrum (joint)
● Force applied to lever moves resistance (muscle = force)
● Consists of axis of rotation, motive/applied force, resisted force
● First class Lever (MAR)
○ Axis in center, motive on one side, resistance on another
■ Like see-saw, antagonist vs agonist muscle
● Second Class Lever (ARM)
○ Resistance in middle, axis is first, motive at end
■ Push ups: feet are the axis, resistance is the center of mass and the
motive are when the arms push up
● Third Class Lever (AMR)
○ Axis is at one end, motive in the middle, resistance at the end
■ Most joints are like this
● Advantages: good ROM and speed
● Disadvantages: force produced
● Mechanical advantage vs disadvantage ratio
○ Mechanical advantage (MA) = Lever arm motive/lever arm resistance
■ MA < 1: disadvantage
● Muscle force greater than resisted
○ Line of action close to axis = shorter lever arm
■ MA > 1: advantage
● Some 1st class lever and all 2nd class levers
○ Muscle force less than resisted force
○ Farther from axis = higher distance moved = higher
velocity
Angular Motion: rotation around a fixed point, within our outside a body
● Measured in degrees, revolutions: 1 = 360 degrees (qualitative)
● Radians: 1 Rad = 57.3 degrees
○ Arc length/radius, radius is dimensionless
○ π rad = 180 degrees
● Distance: angular change in path of motion → analogous to linear distance
● Displacement: final - initial position (indicates direction)
● Speed vs Velocity
○ (ω) = ΔӨ/t ← velocity
○ (a) = Δω/t ← acceleration
● Linear vs angular relationship: motion of any part of body can be explained in linear
terms
○ Need axis, radius of rotation, and kinematics in radians
○ d = Өr ← use radians for Ө
■ Higher radius of rotation = higher linear displacement
, ○ Vt = ωr ← radians for ω, linear velocity of rotating object is tangential to path of
motion
■ Longer radius = more velocity (longer golf club = more distance)
■ Using full extension, increase radius length = more velocity
○ Linear Tangential velocity: vt = (angular velocity) (radius)
■ Change degrees to rad for angular velocity
○ radial acceleration at the instant prior to the point of release: (ω^2)r or (vt^2)/r
Angular Acceleration: acceleration of a body in angular motion which may be resolved into its
components
● Radial: centripetal (toward center)
○ Object must be forced to follow a curved path
○ Change in direction = change in velocity = acceleration occurs
■ Acceleration to required to keep body in curved path
○ Hammer Throw/Throwing in general
■ Ball follows curved path from restraining force of arm
■ The restraining for causes ar toward center of curved path
● ar = v^2/r ← radial acceleration equation
○ Lower the radius = higher radial acceleration
● Release = 0 ar, ball follows path of tangent center of curved path
○ Banked turns in driving
■ Allows sharper turn without decreasing speed
■ Addition centripetally directed force
○ Directed towards center along curved pathway (representing change in direction)
■ Linear speed of an object traveling a curved path remains constant
■ Direction constantly changes = velocity constantly changes = radial
acceleration occurs
● Caused by GRF directed to center of turn
● Tangential: change in linear for a body traveling curved path
Angular Kinetics: causes of angular motions
● Center of Mass: mass or weight is concentrated
○ Equilibrium: equal torque on each side of fulcrum
○ Index of total body motion: Track center of gravity during motion
■ Either whole body or segments: % body height or %segment length
● Location shows where body respond to external forces
■ Center of gravity (COG) changes as body moves
● Balance Method: weight and vertical reaction force at fulcrum must be in same plane
○ High jump: manipulates center of gravity
■ As they reach higher height, without raising COG, therefore easier to
make jump
● Suspension method: same as balance method, easier to accomplish at fulcrum on top
● MRI Reconstruction: high cost, big and bulky, impractical
○ Reconstructs the the tissues in imaging
● Segmental Method: determine center of gravity for each segment experimentally
○ Center of gravity/segment length = ratio
