Kinematic Analysis of Planar Mechanisms
This chapter explains link velocity and acceleration components in planar space, the Newton–Raphson method for a set of two simultaneous equations, vector-loop-based displacement, acceleration equation formulation and solution, kinematics of mechanism link locations of interest, and instant centers in relative planar motion. It discusses instant center generation and application in velocity analysis, centrode generation and application in coupler motion replication, configurations of closed-loop mechanisms, relationships between general angular velocity and time, and cognate construction and application. The chapter formulates the kinematic equations for the planar four-bar, slider-crank, geared five-bar, Watt II, and Stephenson III mechanisms. A single planar four-bar velocity equation is derived by differentiating the planar four-bar displacement equation. The solutions calculated from the planar four-bar displacement, velocity, and acceleration equations can be used in additional equations to calculate the displacement, velocity, and acceleration of any mechanism link location of interest.