Partial Shaking Moment Balancing of Spherical Parallel Robots by a Combined Counterweight and Adjusting Kinematic Parameters Approach

Abstract

Spherical parallel robots (SPR) are widely used in industries and robotic rehabilitation. Designing such systems for better balance properties is still a challenge. This paper presents a work to minimize the shaking moment for a fully force-balanced SPR by combining the counterweight (CW) and adjusting the kinematic parameters (AKP). An approximate model of the shaking moment of the SPR is proposed for computational efficiency (specifically allowing for a gradient-based optimization algorithm available in MATLAB) yet without the loss of much accuracy. The effectiveness of the proposed approach has been confirmed based on simulation, especially with the software system SPACAR due to its high reliability and easy availability. Specifically, the simulation result shows that compared with the unbalanced SPR, the shaking moment of the balanced SPR can decrease by more than 90%. It is worth mentioning that the AKP approach is an excellent example of mechatronics by combining the capability of re-planning the joint motion from the end-effector motion and adjusting the kinematic parameters to redistribute the mass of the whole robot for canceling the shaking force and shaking moment—inertia-induced force and moment to the ground. In short, the main contributions of this paper are: (1) a combined CW and AKP approach to the partial moment balancing of the SPR enhanced with a simplified mathematical model of the shaking moment of the SPR, and (2) a new design of the SPR which can be fully force balanced yet partially moment balanced. A note is taken that the simplified model is under the condition that the parameters of the link have certain geometric relations, which is a limitation of our approach.

Keywords

• spherical parallel robot
• adjusting kinematic parameters
• shaking force
• shaking moment
• balancing