KIN 3309 1nd Edition Lecture 13 Outline of Last Lecture I. Kinetics and Kinematics – a RecapII. Force Plates/Ground Reaction ForcesIII. Force Plates/Ground Reaction Forces DevicesIV. Force Plates/Ground Reaction Forces Data CollectionV. Postural ControlVI. Force Plates/Ground Reaction Forces – ProblemsVII. Motion CaptureVIII. Motion Capture – Stroke Survivors ReachingOutline of Current Lecture I. Angular KinematicsII. Rotational MotionIII. General MotionIV. Instantaneous Center of RotationV. Components of an AngleVI. Measuring AnglesVII. What is a Radian?VIII. Angular VariablesIX. ConversionsX. Types of AnglesXI. Lower Extremity Joint AnglesXII. Segment Angle vs. Joint AngleXIII. Rear Foot AngleXIV. Angular Position, Distance, DisplacementXV. Angular VelocityXVI. Angular Motion VectorsXVII. Angular AccelerationXVIII. Finite DifferentiationXIX. QuizCurrent LectureI. Angular Kinematicsa. Angular kinematics deals with angular motionThese 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. Translationii. Rotationb. Nearly all human movement involves rotation of body segmentsII. Rotational Motiona. Angular Motion: all parts of a body move through the same angle, but do not undergo the same linear displacementIII. General Motiona. Rotation + TranslationIV. Instantaneous Center of Rotationa. With machines, the center of rotation is usually fixedb. This is not the case with human jointsV. Components of an Anglea.VI. Measuring Anglesa. An angle formed by the intersection of two lines (or planes)b. Units of measurementi. 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 radiusb. Circumference = 2pir; therefore, there are 2pi radians in 360 degreesc. Unitless measure of anglesVIII. Angular Variablesa.b.IX. Conversionsa. Comparing degrees and radiansi.b. Converting from degrees to radiansi.c. Converting from radians to degreesi.X. Types of Anglesa. Absolute Angles i. An absolute angle is measured from an external frame of referenceii. The usual convention is to measure the angle anticlockwise from the righthorizontal1. Places a coordinate system at the distal end of point of the segmentiii. Calculating Absolute Angles1. Absolute angles can be calculated from the endpoint coordinates by using the arctangent function2.b. Relative Anglesi. A relative angle is the angle formed between two limb segments1. Referred to as the joint angle or intersegmental angleii. Calculating Relative Angles1. Law of Cosinesa. Useful if the segment lengths are knownb.2. Calculated from two absolute anglesa. Useful if the absolute angles are knownb.XI. Lower Extremity Joint Anglesa. Useful for clinicians to assess functionb. Useful for biomechanists to quantify movementc. Once absolute angles have been quantified, relative angles (joint angles) can be calculatedXII. Segment Angle vs. Joint Anglea.XIII. Rear Foot Anglea. Rear foot angle is a relative anglei. Positive angle for supination (calcaneal inversion)ii. Negative angle for pronation (calcaneal eversionb. Leg and calcaneus angles are absoluteXIV. Angular Position, Distance, Displacementa. Analogous to linear distance and displacementb. Angular positioni. An object’s position relative to a defined spatial reference systemc. Angular distancei. The length of the angular path taken along a pathd. Angular displacementi. The change in angular positionii. A vector!XV. Angular Velocitya. The rate of change of angular positioni. Indicates how fast the angle is changingb. Positive values indicate a counter clockwise rotation negative values indicate a clockwise rotationc. The most common unit of angular velocity is degrees per second but radians per second is the preferred unit (rad/s)XVI. Angular Motion Vectorsa. The right hand thumb rule is used to show the direction of angular motionb.c. A segment rotating counterclockwise (CC) has a positive value and is representedby a vector pointing out of the screend. A segment rotating clockwise (CW) has a negative value and is represented by a vector pointing into the screenXVII. Angular Accelerationa. The rate of change of angular velocityi. Indicates how fast the angular velocity is changingb. The sign of the acceleration vector is independent of the direction of rotationc. The most common unit of angular acceleration is degrees per second squared, but radians per second squared is the preferred unit.XVIII. Finite Differentiationa. Angular velocity and acceleration can be obtained from angular displacement data by finite differentiationb. Note that this is the first central differences methodc.XIX. Quiza. An absolute angle is measured from:i. The absolute value of a joint angleii. The difference between two angles (this is relative angle)iii. The external frame of referenceiv. Always positivev. Is always positiveb. A relative anglei. The difference between two anglesii. Can be positive or negativec. 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 jointd. Given the stick figure, which of angle classifies as a relative angle?i. Be. Given the stick figure, which of angle classifies as a joint angle/relative angle?i. C; b and d are describing absolute anglef. The following coordinates were digitized fro the right lower extremity of a personwalking. Hip (4,10); KNEE (6,4); ANKLE (5,0)i. 1. Calculate the segment angle of the thigh and leg1. 76 degrees for the leg2. 108.4 degrees for the thigh (absolute angle) ii. 2. Calculate the knee joint angle1. 32.47(flexion)g. Angular displacement isi. The change in angular position and the direction of the change (vector)ii. The length of the angular path taken along a pathiii. The rate of change in angular position (angular velocity, vector)iv. The scalarh. If angular velocity is decreasing, angular acceleration must be:i. Negativeii. In the opposite direction as the velocity iii. Constant iv. Changingi. Angular acceleration is: i. The rate of change of angular velocityii. The rate of change of angular displacement (angular velocity)iii. The rate of change of angular distanceiv. The rate of change of angular positionv. Know all these