illinois state university chapter 6 angular kinematics describing objects in angular motion

Illinois State University

Chapter 6

Angular Kinematics

Describing Objects in Angular Motion


Angular Motion

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


Angles

• An angle is formed by the An angle is formed by the intersection of two lines, two intersection of two lines, two planes, or a line and a plane.planes, or a line and a plane.


Measuring angles

Relative versus absolute angles:Relative versus absolute angles:• Relative angle Relative angle - angle at a joint - angle at a joint

formed between the longitudinal formed between the longitudinal axes of adjacent body segments. axes of adjacent body segments.

• Relative angles should be Relative angles should be measured on the same side of a measured on the same side of a given joint. given joint.


Measuring angles

• The straight, fully extended The straight, fully extended position at a joint is regarded as 0 position at a joint is regarded as 0 degrees. degrees.

• When joint ROM is quantified, it is When joint ROM is quantified, it is the relative joint angle that is the relative joint angle that is measured.measured.


Measuring angles

• Absolute angle Absolute angle - angular - angular orientation of a body segment with orientation of a body segment with respect to a fixed line of reference. respect to a fixed line of reference.

• Absolute angles should be Absolute angles should be consistently measured in the same consistently measured in the same direction from a single reference - direction from a single reference - either horizontal or vertical.either horizontal or vertical.


Measuring angles

• The relative angle at the knee is The relative angle at the knee is measured between adjacent body measured between adjacent body segments and the absolute angle segments and the absolute angle of the trunk is measured with of the trunk is measured with respect to the right horizontal.respect to the right horizontal.


Tools for measuring body angles

• GoniometersGoniometers are commonly used are commonly used by clinicians for direct by clinicians for direct measurement of relative joint measurement of relative joint angles on a live human subject.angles on a live human subject.


Tools for measuring body angles

• Other instruments available for Other instruments available for quantifying angles relative to the quantifying angles relative to the human body are the human body are the electrogoniometer and the electrogoniometer and the Leighton flexometer.Leighton flexometer.


Instant center of rotation

• The location of the exact center of The location of the exact center of rotation at the joint changes rotation at the joint changes slightly when joint angle changes. slightly when joint angle changes.

• The instant center is the precisely The instant center is the precisely located center of rotation at a joint located center of rotation at a joint at a given instant in time.at a given instant in time.


(a) Laser scan. (b) Body segments. (c) Joint centers.


Angular distance and displacement:

• Angular displacement is measured Angular displacement is measured as the sum of all angular changes as the sum of all angular changes undergone by a rotating body. undergone by a rotating body.

• It is the change in angular position It is the change in angular position and is defined by both magnitude and is defined by both magnitude and direction (vector quantity). and direction (vector quantity).


Angular kinematic relationships

• The counterclockwise direction is The counterclockwise direction is regarded as positive, and the regarded as positive, and the clockwise direction is regarded as clockwise direction is regarded as negative.negative.



• Three units of measure are Three units of measure are commonly used to represent commonly used to represent angular displacement and angular angular displacement and angular distance. distance.

• The degree, the radian (equal to The degree, the radian (equal to 57.3 degrees), and the revolution. 57.3 degrees), and the revolution.



• Radians are often quantified in Radians are often quantified in multiples of pi. multiples of pi.

• Pi is a mathematical constant Pi is a mathematical constant equal to approximately 3.14, which equal to approximately 3.14, which is the ratio of the circumference to is the ratio of the circumference to the diameter of a circle.the diameter of a circle.


Angular speed and velocity

• Angular speed Angular speed is a scalar quantity is a scalar quantity and is defined as the angular and is defined as the angular distance covered divided by the time distance covered divided by the time interval over which the motion interval over which the motion occurred.occurred.

• Angular velocity Angular velocity is calculated as the is calculated as the change in angular position or the change in angular position or the angular displacement that occurs angular displacement that occurs during a given period of time.during a given period of time.


Angular speed and velocity

• Units of angular speed and angular Units of angular speed and angular velocity are degrees per second velocity are degrees per second (deg/s), radians per second (rad/s), (deg/s), radians per second (rad/s), revolutions per second (rev/s), and revolutions per second (rev/s), and revolutions per minute (rpm).revolutions per minute (rpm).


Angular acceleration

• The change in angular velocity The change in angular velocity occurring over a given time.occurring over a given time.

• Units are degrees per second Units are degrees per second squared (deg/ssquared (deg/s22), rad/s), rad/s22, and rev/s, and rev/s22..


Angular Kinematics

• Angular motion vectors:Angular motion vectors:

• Right hand rule Right hand rule - procedure for - procedure for identifying the direction of an identifying the direction of an angular motion vector.angular motion vector.


Average versus instantaneous angular

quantities• Angular speed, velocity, and Angular speed, velocity, and

acceleration may be calculated as acceleration may be calculated as instantaneous or average values, instantaneous or average values, depending on the length of the depending on the length of the time interval selected.time interval selected.

= = / / tt


Relationships between linear and angular displacement

• Radius of rotation Radius of rotation - distance from the - distance from the axis of rotation to a point of interest axis of rotation to a point of interest on a rotating body.on a rotating body.

• The greater the distance a given point The greater the distance a given point on a rotating body is located from the on a rotating body is located from the axis of rotation, the greater the linear axis of rotation, the greater the linear displacement undergone by that displacement undergone by that point.point.– P 152 Fig 6.7P 152 Fig 6.7


Relationships between linear and angular velocity

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


Relationships between linear and angular velocity

• With all other factors held With all other factors held constant, the greater the radius of constant, the greater the radius of rotation at which a swinging rotation at which a swinging implement hits a ball, the greater implement hits a ball, the greater the linear velocity imparted to the the linear velocity imparted to the ball.ball.


Relationships between linear and angular acceleration

• The acceleration of a body in The acceleration of a body in angular motion may be resolved angular motion may be resolved into two perpendicular linear into two perpendicular linear acceleration components. acceleration components.

• These components are directed These components are directed along and perpendicular to the along and perpendicular to the path of angular motion at any path of angular motion at any point in time.point in time.



• Tangential acceleration Tangential acceleration - component of - component of angular acceleration directed along a angular acceleration directed along a tangent to the path of motion that tangent to the path of motion that indicates change in linear speed.indicates change in linear speed.

• At the instant that a thrown ball is At the instant that a thrown ball is released, its tangential and radial released, its tangential and radial accelerations become equal to 0 accelerations become equal to 0 because a thrower is no longer because a thrower is no longer applying force.applying force.



• The second component of angular The second component of angular acceleration represents the rate acceleration represents the rate change in direction of a body in change in direction of a body in angular motion. angular motion.

• This component is called This component is called radial radial accelerationacceleration, and is always , and is always directed toward the center of directed toward the center of curvature.curvature.



• An increase in linear velocity or a An increase in linear velocity or a decrease in the radius of curvature decrease in the radius of curvature increases radial acceleration increases radial acceleration (choking up on a bat). (choking up on a bat).

• Thus, the smaller the radius of Thus, the smaller the radius of curvature, the more difficult it is curvature, the more difficult it is for a cyclist to negotiate the curve for a cyclist to negotiate the curve at a high velocity.at a high velocity.


Centripetal acceleration

• The linear acceleration directed The linear acceleration directed toward the axis of rotation.toward the axis of rotation.

• Centripetal force Centripetal force is the force that is the force that causes centripetal acceleration.causes centripetal acceleration.


Anatomical Anatomical MovementMovement

TerminologyTerminology


Analyzing Human Movement


• In order to analyze motion, we In order to analyze motion, we have to be able to consistently have to be able to consistently describe it.describe it.

• We need to accurately describe We need to accurately describe which body parts are moving and which body parts are moving and the direction(s) in which they are the direction(s) in which they are moving.moving.



•consistent descriptive terms

•accurately describe actions

•identify critical actions


Standard reference terminology:

Anatomical reference position.

Is this position neutral?

“palms forward” requires muscle activity


Directional terms:

• SuperiorSuperior • InferiorInferior


Directional terms:

• Superior Superior • AnteriorAnterior

• InferiorInferior• PosteriorPosterior


Directional terms:

• Superior Superior • AnteriorAnterior• MedialMedial

• InferiorInferior• PosteriorPosterior• LateralLateral


Directional terms:

• Superior Superior • AnteriorAnterior• MedialMedial• ProximalProximal• SuperficialSuperficial• InferiorInferior• PosteriorPosterior• LateralLateral• DistalDistal• DeepDeep


Anatomical reference planesCardinal planes: Cardinal planes: • Sagittal plane Sagittal plane • Frontal plane Frontal plane • Transverse plane Transverse plane • Oblique planesOblique planes

http://www.sohp.soton.ac.uk/biosci/anatomy1.htm


Anatomical Reference Axes

• Medio-lateral (ML) axis (frontal, Medio-lateral (ML) axis (frontal, transversetransverse))

• Anteroposterior (AP) axis (sagittal Anteroposterior (AP) axis (sagittal axis)axis)

• Longitudinal axis (vertical)Longitudinal axis (vertical)

• Axes are always perpendicular to Axes are always perpendicular to their respective plane of motion.their respective plane of motion.


Joint Movement Terminology

Sagittal plane movements:• Flexion Flexion • Extension Extension • Hyperextension Hyperextension • Dorsiflexion Dorsiflexion • Plantar flexionPlantar flexion

Axis????


Frontal plane movements

• Abduction Abduction • Adduction Adduction • Lateral flexion - sideways rotation Lateral flexion - sideways rotation

of the trunk.of the trunk.• Elevation of the shoulder girdle. Elevation of the shoulder girdle. • Depression of the shoulder girdle.Depression of the shoulder girdle.

Axis????


Frontal plane movements

• Radial deviation - rotation of the Radial deviation - rotation of the hand at the wrist in the frontal hand at the wrist in the frontal plane toward the thumb. plane toward the thumb.

• Ulnar deviation - rotation of the Ulnar deviation - rotation of the hand at the wrist in the frontal hand at the wrist in the frontal plane toward the little finger.plane toward the little finger.


Frontal Plane Movements

• Eversion of the foot - outward Eversion of the foot - outward rotation of the sole of the foot. rotation of the sole of the foot.

• Inversion of the foot - inward Inversion of the foot - inward rotation of the sole of the foot. rotation of the sole of the foot.


Transverse plane movements:

• Left rotation of the head, neck, and Left rotation of the head, neck, and trunk.trunk.

• Right rotation of the head, neck, Right rotation of the head, neck, and trunk.and trunk.

• Medial rotation of the arm or leg. Medial rotation of the arm or leg.

Axis????


Transverse plane movements:

• Lateral rotation of the arm or leg.Lateral rotation of the arm or leg.• Supination and pronation of the Supination and pronation of the

forearm.forearm.• Horizontal abduction and Horizontal abduction and

adductionadduction– horizontal extension and flexionhorizontal extension and flexionAxis????


Special movements:

• Circumduction - combination of Circumduction - combination of flexion/extension, flexion/extension, abduction/adductionabduction/adduction– finger circling in a raised position.finger circling in a raised position.– hiphip– kneeknee


Special Movements

• SupinationSupination of the foot - inversion, of the foot - inversion, adduction, and plantar flexion.adduction, and plantar flexion.

• PronationPronation of the foot - eversion, of the foot - eversion, abduction, and dorsiflexion. abduction, and dorsiflexion.

illinois state university chapter 6 angular kinematics describing objects in angular motion

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