Kinematic analysis of linkages based in finite elements and the geometric stiffness matrix

This paper presents a numerical approach to rigid body linkage kinematics, based on a reduced form of the stiffness matrix and in structural analysis concepts. This matrix may be referred to as geometric stiffness matrix, or simply as geometric matrix. It is derived from basic nodes and length constraints, and provides full information on the kinematic properties of any linkage, including positions, velocities, accelerations, jerks and singular positions. This approach offers a number of major advantages, especially where simplicity and generality are concerned. The computational cost is also very low, because of the simplicity of the numerical calculations and the reduced dimensions of the matrices involved.