Higher order kinematic formulas and its numerical computation employing dual numbers

Abstract

In the analysis of robots and mechanisms, the computation of velocities and accelerations is frequently needed. In other cases, higher-order kinematic formulas such as the jerk and the jounce/snap—the third and fourth-order time derivative of the position vector, respectively—are also needed. While procedures for computing velocity and accelerations can be found elsewhere in the literature, the computations of the jerk and especially of the jounce/snap are not so common. In this study, a novel formulation to compute all kinematic quantities up to the fourth order, based on the dual number is presented. In dual number formalism, kinematic analysis equations are computed automatically once the position vector is constructed. This provides a concise and efficient method to conduct kinematic analysis. To prove the validity of the implemented formulation, we compute the velocity, acceleration, jerk, and jounce/snap for the end effector of the RC robot manipulator. In addition, we compute the jerk and the jounce/snap for the coupler point of the spherical 4 R mechanism.

Keywords:

• Higher order derivatives
• kinematic formulas
• robots and mechanisms
• dual numbers