KIN 3309 1nd Edition Lecture 13 Outline of Last Lecture I II III IV V VI VII VIII Kinetics and Kinematics a Recap Force Plates Ground Reaction Forces Force Plates Ground Reaction Forces Devices Force Plates Ground Reaction Forces Data Collection Postural Control Force Plates Ground Reaction Forces Problems Motion Capture Motion Capture Stroke Survivors Reaching Outline of Current Lecture I Angular Kinematics II Rotational Motion III General Motion IV Instantaneous Center of Rotation V Components of an Angle VI Measuring Angles VII What is a Radian VIII Angular Variables IX Conversions X Types of Angles XI Lower Extremity Joint Angles XII Segment Angle vs Joint Angle XIII Rear Foot Angle XIV Angular Position Distance Displacement XV Angular Velocity XVI Angular Motion Vectors XVII Angular Acceleration XVIII Finite Differentiation XIX Quiz Current Lecture I Angular Kinematics a Angular kinematics deals with angular motion These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute i Translation ii Rotation b Nearly all human movement involves rotation of body segments II Rotational Motion a Angular Motion all parts of a body move through the same angle but do not undergo the same linear displacement III General Motion a Rotation Translation IV Instantaneous Center of Rotation a With machines the center of rotation is usually fixed b This is not the case with human joints V Components of an Angle a VI Measuring Angles a An angle formed by the intersection of two lines or planes b Units of measurement i Degrees arbitrary units ii Radians fundamental ratio iii Revolutions one revolution 360 degrees VII What is a Radian a One radian is the angle at the center of a circle described by an arc equal to the length of the radius b Circumference 2pir therefore there are 2pi radians in 360 degrees c Unitless measure of angles VIII Angular Variables a b IX Conversions a Comparing degrees and radians i b Converting from degrees to radians i c Converting from radians to degrees i X Types of Angles a Absolute Angles i An absolute angle is measured from an external frame of reference ii The usual convention is to measure the angle anticlockwise from the right horizontal 1 Places a coordinate system at the distal end of point of the segment iii Calculating Absolute Angles 1 Absolute angles can be calculated from the endpoint coordinates by using the arctangent function 2 b Relative Angles i A relative angle is the angle formed between two limb segments 1 Referred to as the joint angle or intersegmental angle ii Calculating Relative Angles 1 Law of Cosines a Useful if the segment lengths are known b 2 Calculated from two absolute angles a Useful if the absolute angles are known b XI Lower Extremity Joint Angles a Useful for clinicians to assess function b Useful for biomechanists to quantify movement c Once absolute angles have been quantified relative angles joint angles can be calculated XII Segment Angle vs Joint Angle a XIII Rear Foot Angle a Rear foot angle is a relative angle i Positive angle for supination calcaneal inversion ii Negative angle for pronation calcaneal eversion b Leg and calcaneus angles are absolute XIV Angular Position Distance Displacement a Analogous to linear distance and displacement b Angular position i An object s position relative to a defined spatial reference system c Angular distance i The length of the angular path taken along a path d Angular displacement i The change in angular position ii A vector XV XVI Angular Velocity a The rate of change of angular position i Indicates how fast the angle is changing b Positive values indicate a counter clockwise rotation negative values indicate a clockwise rotation c The most common unit of angular velocity is degrees per second but radians per second is the preferred unit rad s Angular Motion Vectors a The right hand thumb rule is used to show the direction of angular motion b c A segment rotating counterclockwise CC has a positive value and is represented by a vector pointing out of the screen d A segment rotating clockwise CW has a negative value and is represented by a vector pointing into the screen XVII Angular Acceleration a The rate of change of angular velocity i Indicates how fast the angular velocity is changing b The sign of the acceleration vector is independent of the direction of rotation c The most common unit of angular acceleration is degrees per second squared but radians per second squared is the preferred unit XVIII Finite Differentiation a Angular velocity and acceleration can be obtained from angular displacement data by finite differentiation b Note that this is the first central differences method c XIX Quiz a An absolute angle is measured from i The absolute value of a joint angle ii The difference between two angles this is relative angle iii The external frame of reference iv Always positive v Is always positive b A relative angle i The difference between two angles ii Can be positive or negative c Given the stick figure which of angle classifies as a distal end absolute angle QQ i C because it comes from the outside the thigh angle in respect to the knee joint A is the proximal joint d Given the stick figure which of angle classifies as a relative angle i e angle joint i B Given the stick figure which of classifies as a angle relative angle C b and d are describing absolute angle f The following coordinates were digitized fro the right lower extremity of a person walking Hip 4 10 KNEE 6 4 ANKLE 5 0 i 1 Calculate the segment angle of the thigh and leg 1 76 degrees for the leg 2 108 4 degrees for the thigh absolute angle ii 2 Calculate the knee joint angle 1 32 47 flexion g Angular displacement is i The change in angular position and the direction of the change vector ii The length of the angular path taken along a path iii The rate of change in angular position angular velocity vector iv The scalar h If angular velocity is decreasing angular acceleration must be i Negative ii In the opposite direction as the velocity iii Constant iv Changing i Angular acceleration is i The rate of change of angular velocity ii The rate of change of angular displacement angular velocity iii The rate of change of angular distance iv The rate of change of angular position v Know all these definitions