ME321 Kinematics and Dynamics of Machines Steve Lambert Mechanical Engineering, U of Waterloo 12/9/2018

Kinematics and Dynamics Position Analysis Velocity Analysis Acceleration Analysis Force Analysis We will concentrate on four-bar linkages 12/9/2018

Acceleration Analysis Use vector loop equations Vector equations can be expressed in general form, or specialized for planar problems Graphical Solutions Vector Component Solutions Complex Number Solutions (in text) 12/9/2018

Vector Equations 12/9/2018

Vector Equations for Velocity Differentiate Position Vector with respect to Time 12/9/2018

Vector Equation for Acceleration Differentiate velocity equation: To obtain acceleration relation: 12/9/2018

Acceleration Equations Where: - Acceleration of origin - Acceleration in local frame - Coriolis acceleration - Angular acceleration - Centripetal acceleration 12/9/2018

Planar Velocity Equations Assume: Motion is restricted to the XY plane Local frame is aligned with and fixed to link Therefore:  becomes the angular velocity of the link, and local velocity becomes the change in length of the link 12/9/2018

Planar Velocity Equations Becomes: 12/9/2018

Planar Acceleration Equations 12/9/2018

Application to Four-Bar Linkages 12/9/2018

Graphical Solution 12/9/2018

Vector Component Solution But: and Giving: 12/9/2018

Coriolis Acceleration 12/9/2018

Coriolis Direction 12/9/2018