# UMass Amherst KIN 296 - angular-kinematics (4) (11 pages)

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- School:
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- Course:
- Kin 296 - Independent Study

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Angular Kinematics of Human Movement Ch 9 Angular Measures Relative versus Absolute Angles Angular or Rotational Motion Angular or rotational motion occurs when an object moves in an arc about an axis The axis may be real or imaginary but will always be oriented perpendicular to the plane in which the rotation occurs Angular Kinematic Quantities Angular Position Displacement Angular Velocity Angular Acceleration Relationship between Linear Angular Motion Copyright 2017 Brian R Umberger Ph D University of Massachusetts Amherst Angular vs Linear Motion real axis imaginary axis Angular vs Curvilinear Motion Rectilinear Motion Angular Motion Angular Motion Curvilinear Motion P1 P2 P1 Curvilinear Motion P3 P2 P3 lines are different lengths lines are the same length 1 Absolute Relative Angles Absolute Relative Angles Absolute Segment Angles Relative Joint Angles Angles measured between the longitudinal axis of a body segment and a fixed reference line Anatomically based angles measured between the longitudinal axes of adjacent body segments Example thigh angle relative to the horizontal Examples knee joint angle elbow angle Measurement Units Measurement Units Angles are typically measured in degrees For some calculations the required unit of measure for angles is the radian One full circle 360 Angles are measured so that counterclockwise motion is considered to be positive Since a radian is a length of the arc divided by a length of the radius a radian is a dimensionless number circumference 2 r Therefore there are 2 radians in a circle 2 Measuring Body Angles Goniometer One arm fixed to protractor at 0 deg Other arm free to rotate Center of goniometer over joint center Arms aligned over longitudinal axes Measuring Body Angles markers placed at segment endpoints segment endpoints are used to define segments and joints Segments Pelvis Trunk Electrogoniometer elgon Hip Thigh Can be used to record joint angles dynamically Knee Inclinometers Leg Provides absolute angles of body segments Foot Absolute or Segmental Angles Absolute or Segmental Angles Compute angle of inclination of a segment relative to a reference frame fixed at the distal end Compute the angle of inclination of the leg segment relative to the right horizontal given the XY coordinates of the knee and ankle Pelvis Trunk Joints Angle is measured counterclockwise from the right horizontal Thigh tan yprox ydist xprox xdist Leg tan 1 yprox ydist xprox xdist Ankle leg tan 1 yprox ydist xprox xdist leg tan 1 0 51 0 09 1 42 1 09 1 42 0 51 leg tan 1 0 42 0 33 Leg leg leg tan 1 1 2727 leg 51 8 Foot 1 09 0 09 3 Relative or Joint Angles Relative or Joint Angles Joint angles are computed as the difference between the angles of the segments that form the joint Compute the knee joint angle as the difference between the thigh and leg segment angles trunk thigh leg foot trunk Angles are expressed relative to the anatomical position hip thigh trunk flexion extension knee thigh leg flexion extension ankle leg foot 90 knee thigh leg knee 86 1 51 8 34 3 86 1 thigh 51 8 leg dorsi plantar knee foot This is a positive values so it means that the knee is flexed 34 3 from the anatomical position It would be equally correct to say that the knee joint angle is 145 7 180 34 3 Sagittal plane joint angles during ablebodied human walking Some people with cerebral palsy can t flex or extend their knee very well interventions include surgically lengthening the rectus femoris and or transferring the location of the RF insertion Solid lines are for normal walking Dashed and dotted lines are for walking with 20 slower and 20 quicker strides than normal normal patient of gait cycle pre surgery knee joint angle deg Knee Joint Angle Stiff Knee Gait knee joint angle deg Joint Angles of gait cycle post surgery 4 Joint Angles Joint Angles Clinically relevant joint angles are not limited to the sagittal plane Clinically relevant joint angles are not limited to the sagittal plane Q angle right limb front view rearfoot angle right limb rear view The Q angle tends to be larger in women than in men due to a wider pelvis relative to leg length Excessive pronation of the ankle has been linked with knee pain in running A large Q angle may predispose a person to develop patellofemoral pain May be possible to control this using orthotics Joint Angles Angular Displacement Clinically relevant joint angles are not limited to the sagittal plane Angular displacement is difference in initial final angular positions Non contact ACL Injury A suspected mechanism of noncontact ACL injury is the combination of femur adduction with simultaneous knee abduction and ankle eversion Places strain on the ACL Hewett et a 2005 Counterclockwise is positive Clockwise is negative Units are degrees radians or revolutions angular position ang posf ang posi or f i For human joints direction can also be indicated with appropriate terminology flexion adduction etc 5 Angular Distance Displacement Angular Speed Velocity Similar distinction as with linear motion Angular speed is how fast something is rotating Positive Direction 40 angular speed angular distance change in time Angular displacement is final position minus initial position while angular distance accounts for whole path of motion Angular velocity is rate of change in ang pos 70 50 angular dist 160 t 0 angular disp 40 30 ang vel angular displacement change in time t 10 Appropriate Units deg s rad s rev s rpm Angular Speed Velocity Angular Acceleration To calculate angular velocity Angular acceleration is the rate of change of angular velocity ang posf ang posi t timef timei Angular velocity is a vector quantity direction of motion must be specified positive negative e g 6 deg s clockwise counterclockwise e g 15 rad s CW joint specific e g 90 deg s into flexion ang accel change in ang vel change in time t To calculate angular acceleration ang accel ang velf ang veli timef timei Appropriate Units deg s2 rad s2 rev s2 6 Angular Kinematics Angular Kinematics Equations on the preceding slides give the average angular velocity and acceleration Instantaneous values can be approximated using the same finite difference approach that we used previously Angular Motion Vectors Follow the right hand rule We can also integrate the angular acceleration to get angular velocity and integrate angular velocity to get angular position Differentiation What would the angular velocity and angular acceleration vectors look like for this skater Postive ang accel

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