Abstract
The kinematics with the instantaneous motion and statics of a manipulator has generally been proven algebraically. The algebraic solutions give very simple and straightforward results but the solutions do not have any meaning in physics or geometry. Therefore it is not easy to extend the algebraic results to design or control a robotic manipulator efficiently. Recently, geometrical approach to define the instantaneous motion or static relation of a manipulator is popularly researched and the results have very strong advantages to have a physical insight in the solution. In this paper, the instantaneous motion and static relation of a planar manipulator are described by geometrical approach, specifically by an axis screw and a line screw. The mass center of a triangle with weight and a perpendicular distance between the two screws are useful geometric measures for geometric analysis. This study provides a geometric interpretation of the kinematics and statics of a planar manipulator, and the method can be applied to design or control procedure from the geometric information in the equations.
