Closed-Form Dynamic Formulation of a General 6-P US Robot

Abstract

The 6-P US parallel manipulator can be used as a good alternative for the 6-UP S manipulator, known as Stewart platform. 6-P US parallel robots may be designed and manufactured in various architectures with different attributes. In this paper, to assess all the possible architectures of the 6-P US with respect to both workspace and dynamic performance, a general geometry is first defined. Using Newton-Euler method, the dynamic model of the general 6-P US robot is derived and its closed-form dynamic equations are presented. More accurate formulation is obtained by considering all robot’s component inertia as well as including the angular velocity and acceleration vectors of the robot’s legs. Moreover, the effect of neglecting link inertia of the 6-P US robot is studied for different payload to link mass ratios. The closed-form model includes dynamic matrices of the robot which can conveniently be used for model based control techniques. Two trajectories are considered and the derived dynamic formulation is verified using a commercial multibody dynamics software. Finally, four case studies covering the well-known architectures of the 6-P US manipulator, including the Hexaglide and the HexaM, are compared based on the robot workspace and forces of the actuators. The results indicates that amongst the studied designs of the 6-P US robot, the architecture with rails leaning outside provides the best performance and therefore can be considered as a competitor for the conventional Stewart platforms.