1. Illinois State University Chapter 6 Angular Kinematics Describing Objects in Angular Motion

2. Illinois State University Angular Motion In angular motion, or rotational motion around an axis, the axis of rotation is a line, real or imaginary, oriented perpendicular to the plane in which the rotation occurs, like the axle for the wheels of a cart.In angular motion, or rotational motion around an axis, the axis of rotation is a line, real or imaginary, oriented perpendicular to the plane in which the rotation occurs, like the axle for the wheels of a cart.

3. Illinois State University Angles An angle is formed by the intersection of two lines, two planes, or a line and a plane.An angle is formed by the intersection of two lines, two planes, or a line and a plane. 

4. Illinois State University Measuring angles Relative versus absolute angles: Relative angle - angle at a joint formed between the longitudinal axes of adjacent body segments.Relative angle - angle at a joint formed between the longitudinal axes of adjacent body segments. Relative angles should be measured on the same side of a given joint.Relative angles should be measured on the same side of a given joint.

5. Illinois State University Measuring angles The straight, fully extended position at a joint is regarded as 0 degrees.The straight, fully extended position at a joint is regarded as 0 degrees. When joint ROM is quantified, it is the relative joint angle that is measured.When joint ROM is quantified, it is the relative joint angle that is measured.

6. Illinois State University Measuring angles Absolute angle - angular orientation of a body segment with respect to a fixed line of reference.Absolute angle - angular orientation of a body segment with respect to a fixed line of reference. Absolute angles should be consistently measured in the same direction from a single reference - either horizontal or vertical.Absolute angles should be consistently measured in the same direction from a single reference - either horizontal or vertical.

7. Illinois State University Measuring angles The relative angle at the knee is measured between adjacent body segments and the absolute angle of the trunk is measured with respect to the right horizontal.The relative angle at the knee is measured between adjacent body segments and the absolute angle of the trunk is measured with respect to the right horizontal.

8. Illinois State University Tools for measuring body angles Goniometers are commonly used by clinicians for direct measurement of relative joint angles on a live human subject.Goniometers are commonly used by clinicians for direct measurement of relative joint angles on a live human subject.

9. Illinois State University Tools for measuring body angles Other instruments available for quantifying angles relative to the human body are the electrogoniometer and the Leighton flexometer.Other instruments available for quantifying angles relative to the human body are the electrogoniometer and the Leighton flexometer.

10. Illinois State University Instant center of rotation The location of the exact center of rotation at the joint changes slightly when joint angle changes.The location of the exact center of rotation at the joint changes slightly when joint angle changes. The instant center is the precisely located center of rotation at a joint at a given instant in time.The instant center is the precisely located center of rotation at a joint at a given instant in time.

11. Illinois State University (a) Laser scan. (b) Body segments. (c) Joint centers.

12. Illinois State University Angular distance and displacement: Angular displacement is measured as the sum of all angular changes undergone by a rotating body.Angular displacement is measured as the sum of all angular changes undergone by a rotating body. It is the change in angular position and is defined by both magnitude and direction (vector quantity).It is the change in angular position and is defined by both magnitude and direction (vector quantity).

13. Illinois State University Angular kinematic relationships The counterclockwise direction is regarded as positive, and the clockwise direction is regarded as negative.The counterclockwise direction is regarded as positive, and the clockwise direction is regarded as negative.

14. Illinois State University Angular kinematic relationships Three units of measure are commonly used to represent angular displacement and angular distance.Three units of measure are commonly used to represent angular displacement and angular distance. The degree, the radian (equal to 57.3 degrees), and the revolution.The degree, the radian (equal to 57.3 degrees), and the revolution.

15. Illinois State University Angular kinematic relationships Radians are often quantified in multiples of pi.Radians are often quantified in multiples of pi. Pi is a mathematical constant equal to approximately 3.14, which is the ratio of the circumference to the diameter of a circle.Pi is a mathematical constant equal to approximately 3.14, which is the ratio of the circumference to the diameter of a circle.

16. Illinois State University Angular speed and velocity Angular speed is a scalar quantity and is defined as the angular distance covered divided by the time interval over which the motion occurred.Angular speed is a scalar quantity and is defined as the angular distance covered divided by the time interval over which the motion occurred. Angular velocity is calculated as the change in angular position or the angular displacement that occurs during a given period of time.Angular velocity is calculated as the change in angular position or the angular displacement that occurs during a given period of time.

17. Illinois State University Angular speed and velocity Units of angular speed and angular velocity are degrees per second (deg/s), radians per second (rad/s), revolutions per second (rev/s), and revolutions per minute (rpm).Units of angular speed and angular velocity are degrees per second (deg/s), radians per second (rad/s), revolutions per second (rev/s), and revolutions per minute (rpm).

18. Illinois State University Angular acceleration The change in angular velocity occurring over a given time.The change in angular velocity occurring over a given time. Units are degrees per second squared (deg/s 2 ), rad/s 2, and rev/s 2.Units are degrees per second squared (deg/s 2 ), rad/s 2, and rev/s 2.

19. Illinois State University Angular Kinematics Angular motion vectors:Angular motion vectors: Right hand rule - procedure for identifying the direction of an angular motion vector.Right hand rule - procedure for identifying the direction of an angular motion vector.

20. Illinois State University Average versus instantaneous angular quantities Angular speed, velocity, and acceleration may be calculated as instantaneous or average values, depending on the length of the time interval selected.Angular speed, velocity, and acceleration may be calculated as instantaneous or average values, depending on the length of the time interval selected.  =  /  t

21. Illinois State University Relationships between linear and angular displacement Radius of rotation - distance from the axis of rotation to a point of interest on a rotating body.Radius of rotation - distance from the axis of rotation to a point of interest on a rotating body. The greater the distance a given point on a rotating body is located from the axis of rotation, the greater the linear displacement undergone by that point.The greater the distance a given point on a rotating body is located from the axis of rotation, the greater the linear displacement undergone by that point. –P 152 Fig 6.7

22. Illinois State University

23. Relationships between linear and angular velocity The same type of relationship exists between the angular velocity of a rotating body and the linear velocity of a point on that body at a given instant in time.The same type of relationship exists between the angular velocity of a rotating body and the linear velocity of a point on that body at a given instant in time.

24. Illinois State University Relationships between linear and angular velocity With all other factors held constant, the greater the radius of rotation at which a swinging implement hits a ball, the greater the linear velocity imparted to the ball.With all other factors held constant, the greater the radius of rotation at which a swinging implement hits a ball, the greater the linear velocity imparted to the ball.

25. Illinois State University Relationships between linear and angular acceleration The acceleration of a body in angular motion may be resolved into two perpendicular linear acceleration components.The acceleration of a body in angular motion may be resolved into two perpendicular linear acceleration components. These components are directed along and perpendicular to the path of angular motion at any point in time.These components are directed along and perpendicular to the path of angular motion at any point in time.

26. Illinois State University Relationships between linear and angular acceleration Tangential acceleration - component of angular acceleration directed along a tangent to the path of motion that indicates change in linear speed.Tangential acceleration - component of angular acceleration directed along a tangent to the path of motion that indicates change in linear speed. At the instant that a thrown ball is released, its tangential and radial accelerations become equal to 0 because a thrower is no longer applying force.At the instant that a thrown ball is released, its tangential and radial accelerations become equal to 0 because a thrower is no longer applying force.

27. Illinois State University Relationships between linear and angular acceleration The second component of angular acceleration represents the rate change in direction of a body in angular motion.The second component of angular acceleration represents the rate change in direction of a body in angular motion. This component is called radial acceleration, and is always directed toward the center of curvature.This component is called radial acceleration, and is always directed toward the center of curvature.

28. Illinois State University Relationships between linear and angular acceleration An increase in linear velocity or a decrease in the radius of curvature increases radial acceleration (choking up on a bat).An increase in linear velocity or a decrease in the radius of curvature increases radial acceleration (choking up on a bat). Thus, the smaller the radius of curvature, the more difficult it is for a cyclist to negotiate the curve at a high velocity.Thus, the smaller the radius of curvature, the more difficult it is for a cyclist to negotiate the curve at a high velocity.

29. Illinois State University Centripetal acceleration The linear acceleration directed toward the axis of rotation.The linear acceleration directed toward the axis of rotation. Centripetal force is the force that causes centripetal acceleration.Centripetal force is the force that causes centripetal acceleration.

30. Illinois State University AnatomicalMovementTerminology

31. Analyzing Human Movement In order to analyze motion, we have to be able to consistently describe it.In order to analyze motion, we have to be able to consistently describe it. We need to accurately describe which body parts are moving and the direction(s) in which they are moving.We need to accurately describe which body parts are moving and the direction(s) in which they are moving.

32. Illinois State University Analyzing Human Movement consistent descriptive terms accurately describe actions identify critical actions

33. Illinois State University Standard reference terminology: Anatomical reference position. Is this position neutral? “palms forward” requires muscle activity

34. Illinois State University Directional terms: SuperiorSuperior InferiorInferior

35. Illinois State University Directional terms: SuperiorSuperior AnteriorAnterior InferiorInferior PosteriorPosterior

36. Illinois State University Directional terms: SuperiorSuperior AnteriorAnterior MedialMedial InferiorInferior PosteriorPosterior LateralLateral

37. Illinois State University Directional terms: SuperiorSuperior AnteriorAnterior MedialMedial ProximalProximal SuperficialSuperficial InferiorInferior PosteriorPosterior LateralLateral DistalDistal DeepDeep

38. Illinois State University Anatomical reference planes Cardinal planes: Sagittal planeSagittal plane Frontal planeFrontal plane Transverse planeTransverse plane Oblique planesOblique planes http://www.sohp.soton.ac.uk/biosci/anatomy1.htm

39. Illinois State University Anatomical Reference Axes Medio-lateral (ML) axis (frontal, transverse )Medio-lateral (ML) axis (frontal, transverse ) Anteroposterior (AP) axis (sagittal axis)Anteroposterior (AP) axis (sagittal axis) Longitudinal axis (vertical)Longitudinal axis (vertical) Axes are always perpendicular to their respective plane of motion.Axes are always perpendicular to their respective plane of motion.

40. Illinois State University Joint Movement Terminology Sagittal plane movements: FlexionFlexion ExtensionExtension HyperextensionHyperextension DorsiflexionDorsiflexion Plantar flexionPlantar flexion Axis????

41. Illinois State University Frontal plane movements AbductionAbduction AdductionAdduction Lateral flexion - sideways rotation of the trunk.Lateral flexion - sideways rotation of the trunk. Elevation of the shoulder girdle.Elevation of the shoulder girdle. Depression of the shoulder girdle.Depression of the shoulder girdle. Axis????

42. Illinois State University Frontal plane movements Radial deviation - rotation of the hand at the wrist in the frontal plane toward the thumb.Radial deviation - rotation of the hand at the wrist in the frontal plane toward the thumb. Ulnar deviation - rotation of the hand at the wrist in the frontal plane toward the little finger.Ulnar deviation - rotation of the hand at the wrist in the frontal plane toward the little finger.

43. Illinois State University Frontal Plane Movements Eversion of the foot - outward rotation of the sole of the foot.Eversion of the foot - outward rotation of the sole of the foot. Inversion of the foot - inward rotation of the sole of the foot.Inversion of the foot - inward rotation of the sole of the foot.

44. Illinois State University Transverse plane movements: Left rotation of the head, neck, and trunk.Left rotation of the head, neck, and trunk. Right rotation of the head, neck, and trunk.Right rotation of the head, neck, and trunk. Medial rotation of the arm or leg.Medial rotation of the arm or leg. Axis????

45. Illinois State University Transverse plane movements: Lateral rotation of the arm or leg.Lateral rotation of the arm or leg. Supination and pronation of the forearm.Supination and pronation of the forearm. Horizontal abduction and adductionHorizontal abduction and adduction –horizontal extension and flexion Axis????

46. Illinois State University Special movements: Circumduction - combination of flexion/extension, abduction/adductionCircumduction - combination of flexion/extension, abduction/adduction –finger circling in a raised position. –hip –knee

47. Illinois State University Special Movements Supination of the foot - inversion, adduction, and plantar flexion. Supination of the foot - inversion, adduction, and plantar flexion. Pronation of the foot - eversion, abduction, and dorsiflexion. Pronation of the foot - eversion, abduction, and dorsiflexion.