Geometrical kinematic and static analyses of planar manipulators using a barycentric formula

Abstract

This study provides a geometric interpretation of the kinematics and statics of a planar manipulator using a barycentric formula. The kinematics with instantaneous motion and statics of a manipulator have recently been proven algebraically. In the past, such studies did not provide any intuition about the equations. Robot designers needed numerical methods or trial-and-error solvers using meaningless equations. In contrast, all algebraic processes have their own geometrical meaning. Geometric analysis provides intuition for designing the linkages of a robot. Screw theory and barycentric formulas were used to find meaningful geometric measures. The kinematics and statics of a manipulator are described by an axis screw and its reciprocal, the line screw. The barycenter of a triangle with edges and the perpendicular distance between the two screws are useful geometric measures for geometric analysis.