Linear Kinematics of Human Movement Ch 8 Basic Kinematic Quantities Position Displacement Distance Velocity Speed Acceleration Differentiation Integration Linear Kinematics of Locomotion Uniform Acceleration Projectile Motion Copyright 2021 Sarah A Roelker Ph D University of Massachusetts Amherst Kinematics Physics Mechanics Other areas of physics Statics Dynamics Kinematics Kinetics Kinematics Describes spatial and temporal components of motion without reference to the forces that caused the motion 1 2 1 Quantifying Human Motion When someone moves runs walks jumps how can we quantify their motion Forms of Motion Linear Angular General 3 4 2 Linear Motion Translation Movement of a body such that all parts of travel exactly the same distance in the same direction in the same amount of time 5 6 3 Linear Motion Translation Rectilinear motion Curvilinear Motion 7 8 Angular Motion Rotation Movement of a body along a circular path about a line in space All parts of the body travel through the same angle in the same direction in the same time This line is known as the axis of rotation and lies at right angles to the plane of motion of the body The axis of rotation may or may not pass through the body itself 4 Angular vs Curvilinear Motion Angular Motion Curvilinear Motion P1 P2 P1 P3 P2 P3 lines are different lengths lines are the same length General Motion Combined linear and angular motion Most human activities involve both linear and angular movement and are thus forms of general motion 9 10 5 Linear Kinematics Physics Mechanics Other areas of physics Statics Dynamics Kinematics Kinetics Linear Angular 11 12 Frames of Reference Global Reference Frame Also called Inertial Frame Fixed Frame xP yP zP Laboratory Reference Frame Y Absolute position of the pelvis in a global reference frame xp yp zp Z X 6 Frames of Reference local or segmental reference frames XT YT ZT joint based reference frames Abd Add Flex Ext Int Ext Rot reference frame fixed to the thigh reference frame fixed in the knee Collecting Kinematic Data Many different types of systems exist for data collection Electrogoniometers 13 14 7 Collecting Kinematic Data Many 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 based 15 16 Phases of a Movement To facilitate analyses it is common to divide a movement sequence into two or more phases 0 60 100 stance and swing phases of the human gait cycle 8 Phases of a Movement To facilitate analyses it is common to divide a movement sequence into two or more phases Phases of a Movement 17 18 9 Phases of a Movement Many discrete movements can be described as consisting of a preparation phase an action phase and a follow though phase preparation action follow through Temporal Analysis The time spent in each phase is one of the most basic descriptions of a movement sequence 0 60 100 Typical values for an adult walking at normal speed Stride 0 92 sec Stance 0 55 sec Swing 0 37 sec Stride 19 20 10 Linear Position Where a point of interest is at a given instant in time Must be expressed in an established reference system position 2 at time 2 x2 y2 center of mass position x1 y1 position 1 at time 1 Y X 21 22 Linear Displacement Distance si si initial position sf final position sf 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 11 Linear 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 23 24 Representing Vectors Vector quantities such as forces are represented graphically using arrows F1 F1 F2 F2 F3 Length of the arrow denotes the magnitude of the vector Orientation of the arrow denotes the direction of the vector 12 Linear Displacement Displacement d or s is calculated as the change in position cid 3033 Example a football player receives a punt exactly in the middle of the field at the 10 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 10 40 His distance would be greater maybe 70 80 yd or more https www on3 com 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 25 26 13 Numerical Example Motion in Positive Direction si 20 m ti 4 s sf 60 m tf 9 s 27 28 Velocity vs Speed Speed is how fast something is moving Velocity v is the rate of change in position cid 2940 cid 2940 units are m s 14 Linear Velocity Example a football player receives a punt exactly in the middle of the field at the ten yard line As he runs down the field he runs laterally 10 yd left then 10 yd right 15 yd left and finally 15 yd right He is tackled at the fifty yard line exactly in the middle of the field It takes him 20s to get to midfield His displacement would be What distance did he run What was his running speed What was his running velocity https www on3 com 29 30 Solution Example a football player receives a punt exactly in the middle of the field at the ten yard line As he runs down the field he runs laterally 10 yd left then 10 yd right 15 yd left and finally 15 yd right He is tackled at the fifty yard line exactly in the middle of the field It takes him 20 s to get to midfield His displacement would be What distance did he run What was his running speed What was his running velocity 15 Velocity Summary Calculation cid 2879 cid 2879 Velocity is a vector quantity Direction of motion must be accounted for Velocity is speed in a specific direction up east etc E g 6 m s i e 6 m s in the negative direction Velocity is defined in each component direction E g 3 m s in x direction and 2 m s in y direction Linear Acceleration 31 32 The pitcher throws a ball to the batter and as a result of contact with the bat the motion of the ball changes What describes the change in motion of an object 16 Acceleration Acceleration is the rate of change of velocity units are m s2 Calculation cid 2879 cid 2879 When velocity is constant acceleration is zero rate of change change