Linear Kinematics of Human Movement Ch 8 Kinematics Physics Part I Basic Kinematic Quantities Position Displacement Distance Velocity Speed Acceleration Other areas of physics Mechanics Statics Dynamics Differentiation Integration Linear Kinematics of Locomotion Kinematics Kinetics Uniform Acceleration Projectile Motion Copyright 2017 Brian R Umberger Ph D University of Massachusetts Amherst More 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 Kinematics Description of motion without reference to the forces that caused the motion Quantifying Human Motion When someone moves runs walks jumps how can we quantify their motion Examples 30 mph is a scalar 30 mph due east is a vector 1 Phases of a Movement Phases of a Movement To facilitate analyses it is common to divide a movement sequence into two or more phases Many discrete movements can be described as consisting of a preparation phase an action phase and a follow though phase 0 60 100 preparation stance and swing phases of the human gait cycle action follow through Temporal Analysis Frames of Reference The time spent in each phase is one of the most basic descriptions of a movement sequence Global reference frame Also called inertial fixed or laboratory reference frame Typical values for an adult walking at normal speed Stride 0 92 sec Stance 0 55 sec Swing 0 37 sec Stride Absolute position of Z the pelvis in a global reference frame xP yP zP Y X 2 Frames of Reference Collecting Kinematic Data local or segmental reference frames Many different types of systems exist for data collection joint based reference frames Electrogoniometers Abd Add XT YT Accelerometers Flex Ext Electromagnetic tracking Optoelectronic systems ZT Video based systems Int Ext Rot Cameras track reflective markers placed on body segments reference frame fixed to the thigh reference frame fixed in the knee Linear Displacement Distance Linear Position center of mass position Where a point of interest is at a given instant in time Must be expressed in an established reference system UMass Biomechanics Lab system is video based position 2 at time 2 si initial position sf final position si x2 y2 x1 y1 sf Y position 1 at time 1 X 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 motion 3 Displacement 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 Velocity Linear Displacement Displacement 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 Velocity Speed How fast is a person or an object moving and in what direction What information do you need to know to determine this Speed is how fast something is moving speed distance or path length change in time Velocity v is the rate of change in position velocity displacement position change in time time v d sf si t t units are m s 4 Linear Acceleration Velocity Speed To calculate velocity velocity positionf positioni timef timei Velocity is a vector quantity direction of motion must be accounted for A person steps off a box and lands on the ground speed plus a direction up east etc 6 m s i e 6 m s in the negative direction velocity for each component direction 3 m s in x direction and 2 m s in y direction The magnitude of his velocity gradually increases as he falls and then rapidly decreases when he contacts the ground What describes these changes in his motion Conditions of Acceleration Acceleration The sign of a velocity or displacement vector tells you the direction of motion Acceleration a is the rate of change of velocity Acceleration change in velocity change in time or To calculate acceleration acceleration velocityf velocityi timef timei a v t However the sign of an acceleration vector by itself tells you little you must also know the direction of motion units are m s2 When velocity is constant acceleration is zero There are four possible cases of acceleration direction direction 5 Case A motion in the pos direction slow jog fast run Case B motion in the pos direction fast run speeding up vel acc Case C motion in the neg direction slow jog speeding up vel acc vel velocity and acceleration vectors Summary motion is in the pos direction so vel is pos velocity is increasing in the pos direction therefore this is a case of positive acceleration fast run slow jog slowing down acc velocity and acceleration vectors Summary motion is in the pos direction so vel is pos velocity is decreasing in the pos direction therefore this is a case of negative acceleration Case D motion in the neg direction slow jog fast run slowing down velocity and acceleration vectors Summary motion is in the neg direction so vel is neg velocity is increasing in the neg direction therefore this is a case of negative acceleration vel acc velocity and acceleration vectors Summary motion is in the neg direction so vel is neg velocity is decreasing in the neg direction therefore this is a case of positive acceleration 6 Conditions of Acceleration Look at the signs of the velocity and acceleration Numerical example slow jog fast run speeding up If the signs are the same then speed is increasing vel acc vel acc speed increasing speed increasing If the signs are different then speed is decreasing vel acc vel acc si 50 m ti 4 s sf 90 m tf 9 s v s t sf si tf ti speed decreasing speed decreasing v 90 50 9 4 8 m s Numerical example fast run Up Next slow jog slowing down vi 10 m s ti 4 s vf 3 m s tf 7 s a v t vf vi tf ti a 3 10 7 4 2 33 m s2 Differentiation Integration Acknowledgement The following individuals have contributed to the materials in these slides R Shapiro PhD University of Kentucky PE Martin PhD Penn State University GE Caldwell PhD University of Massachusetts W