Using transformation matrix to analyze planar mechanism Kinematics

Abstract

Planar mechanism kinematic analysis can be performed either analytically or graphically. Graphical kinematic analysis is considered as a simple, intuitive approach but less accurate because values of kinematic quantities are measured from graphical vector diagrams. Analytical kinematics is a more advanced method thanks to using precise mathematical operations and easy to automate. Currently, there are many analytical kinematic methods introduced in somedocuments in universities but most of them are difficult to use because of complicated application.Finding an appropriate approach to solve more easily kinematic problems for planar mechanisms is a necessary work. By using the transformation matrix and using basic operations for matrix (such as addition, scalar multiplication, and derivative) the position, velocity, and acceleration equationswill be established for a planar mechanism. From these formulas, analytical kinematics can be applied for typical planar mechanisms. The first advantage of this method is able to calculate position, velocity, and acceleration of links and joints accurately at any position of input link. The second is to develop computation process automatically thanks to support from computer program, such as MatLab, Excel. Some chosen examples shown out here aim todemonstrate the transformation matrix application to solve analytical kinematic problems for different planar mechanisms.