1Linear Kinematics of Human Movement (Ch 8)• Basic Kinematic QuantitiesPosition, Displacement, DistanceVelocity, SpeedAcceleration• Differentiation & Integration• Linear Kinematics of Locomotion• Uniform Acceleration / Projectile MotionCopyright © 2017Brian R. Umberger, Ph.D.University of Massachusetts AmherstPart IKinematicsPhysicsMechanicsOther areas of physicsStatics DynamicsKinematics KineticsKinematics: Description of motion, without reference to the forces that caused the motionMore Definitions • Linear kinematics: the description of linear motion (there is either no rotation, or it is not explicitly considered)• Scalars & Vectors:– Scalar: a quantity that has magnitude only– Vector: a quantity that has both magnitude and direction– Examples:• 30 mph is a scalar• 30 mph due east is a vectorQuantifying Human MotionWhen someone moves (runs, walks, jumps…), how can we quantify their motion?2Phases of a MovementTo facilitate analyses, it is common to divide a movement sequence into two or more phasesstance and swing phases of the human gait cycle60%0% 100%Phases of a MovementMany discrete movements can be described as consisting of a preparation phase, an action phase, and a follow-though phasepreparationaction follow-throughTemporal AnalysisThe time spent in each phase is one of the most basic descriptions of a movement sequenceTypical values for an adult walking at normal speed:Stride 0.92 secStance 0.55 secSwing 0.37 secStride%%%Frames of ReferenceAbsolute position of the pelvis in a global reference frameXYZGlobal reference frameAlso called: inertial, fixed, or laboratory reference frame(xP,yP,zP)3Frames of Referencereference frame fixed to the thighlocal or segmental reference framesXTZTYTreference frame fixed in the kneejoint-based reference framesFlex/ExtInt/Ext RotAbd/AddCollecting Kinematic DataMany different types of systems exist for data collection:– Electrogoniometers– Accelerometers– Electromagnetic tracking– Optoelectronic systems– Video-based systems*• Cameras track reflective markers placed on body segments*UMass Biomechanics Lab system is video-basedLinear Position• Where a point of interest is at a given instant in time• Must be expressed in an established reference systemXYposition 1 at time 1position 2 at time 2center of mass position(x1,y1)(x2,y2)Linear Displacement & Distance• Linear displacement (a vector), is the straight line change in position, from initial to final position• Linear distance (a scalar) is measured along the actual path of motionsfsisi= initial positionsf= final position4Displacement & Distance• Both have dimensions of length– Metric (SI): meter, kilometer, centimeter– English: inch, foot, yard, mile• Linear distance– Scalar quantity: no direction specified • Linear displacement– Vector quantity: length & direction required (e.g., left, right, up, & down, north, south, east, & west, positive & negative)Linear DisplacementDisplacement (d or s) is calculated as the change in position:d = change in position = s= sf-si Example: a football player receives a punt exactly in the middle of the field, at the ten yard line. He runs laterally left and right, as well as down the field. He is tackled at the fifty yard line, exactly in the middle of the field.His displacement would be: 50 yd - 10 yd = 40 yd His distance would be greater: maybe 70-80 yd(or more)Linear Velocity• How fast is a person or an object moving, and in what direction?• What information do you need to know to determine this?Velocity & SpeedSpeed is how fast something is movingspeed = distance (or path length)change in timeVelocity (v) is the rate of change in positionvelocity = displacement =  positionchange in time  timev = d = sf-si t  tunits are m/s5Velocity & SpeedTo calculate velocity:velocity = positionf- positionitimef-timei• Velocity is a vector quantity; direction of motion must be accounted for – speed plus a direction (+/-, up, east, etc)6 m/s (i.e., 6 m/s in the negative direction)– velocity for each component direction3 m/s in x-direction and 2 m/s in y-directionLinear AccelerationA person steps off a box and lands on the groundThe magnitude of his velocity gradually increases as he falls, and then rapidly decreases when he contacts the groundWhat describes these changes in his motion?AccelerationAcceleration = change in velocity or a = vchange in time tTo calculate acceleration:acceleration = velocityf-velocityitimef-timeiWhen velocity is constant, acceleration is zero!Acceleration (a) is the rate of change of velocityunits arem/s2Conditions of Acceleration• The “sign” of a velocity or displacement vector tells you the direction of motion• However, the “sign” of an acceleration vector by itself tells you little; you must also know the direction of motion• There are four possible cases of acceleration+ direction− direction6Summary• motion is in the pos (+) direction, so vel is pos (+)• velocity is increasing in the pos (+) direction• therefore, this is a case of positive (+) accelerationCase A: motion in the pos directionslow jog fast runvelocity and acceleration vectorsvel (+) acc (+)speeding upCase B: motion in the pos directionSummary• motion is in the pos (+) direction, so vel is pos (+)• velocity is decreasing in the pos (+) direction• therefore, this is a case of negative (-) accelerationslow jogfast runvel (+) acc (-)slowing downvelocity and acceleration vectorsCase C: motion in the neg directionSummary• motion is in the neg (-) direction, so vel is neg (-)• velocity is increasing in the neg (-) direction• therefore, this is a case of negative (-) accelerationslow jogfast runvel (-) acc (-)speeding upvelocity and acceleration vectorsCase D: motion in the neg directionSummary• motion is in the neg (-) direction, so vel is neg (-)• velocity is decreasing in the neg (-) direction• therefore, this is a case of positive (+) accelerationslow jog fast runvel (-) acc (+)slowing downvelocity and acceleration vectors7Conditions of AccelerationLook at the signs of the velocity and acceleration• If the signs are the same, then speed is increasing+ vel + acc speed increasing- vel - acc speed increasing• If the signs are different, then speed is decreasing+ vel - acc speed decreasing- vel + acc speed decreasingsi= 50 mti= 4 ssf= 90 mtf= 9 sNumerical