ME 321 Kinematics and Dynamics of Machines Steve

ME 321 Kinematics and Dynamics of Machines Steve Lambert Mechanical Engineering, U of Waterloo 6/6/2021

Kinematics and Dynamics l l Position Analysis Velocity Analysis Acceleration Analysis Force Analysis We will concentrate on four-bar linkages 6/6/2021

Acceleration Analysis l l 6/6/2021 Use vector loop equations Vector equations can be expressed in general form, or specialized for planar problems Ô Graphical Solutions Ô Vector Component Solutions Ô Complex Number Solutions (in text)

Vector Equations 6/6/2021

Vector Equations for Velocity Differentiate Position Vector with respect to Time 6/6/2021

Vector Equation for Acceleration Differentiate velocity equation: To obtain acceleration relation: 6/6/2021

Acceleration Equations Where: - Acceleration of origin - Acceleration in local frame - Coriolis acceleration - Angular acceleration - Centripetal acceleration 6/6/2021

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 6/6/2021

Planar Velocity Equations Becomes: 6/6/2021

Planar Acceleration Equations 6/6/2021

Application to Four-Bar Linkages 6/6/2021

Graphical Solution 6/6/2021

Vector Component Solution But: and Giving: 6/6/2021

Coriolis Acceleration 6/6/2021

Coriolis Direction 6/6/2021