Preliminary Analysis and Simulation of a Compact Variable Stiffness Wrist

TL;DR

This work presents a compact 3-DoF parallel wrist that achieves variable stiffness via redundant elastic actuation and operates with only four motors. It develops a comprehensive kinematic and dynamic model (forward, inverse, and differential kinematics; nonlinear static stiffness; Euler-Lagrange dynamics) and introduces a control strategy that independently regulates joint position and stiffness using a Levenberg-Marquardt optimization to match Cartesian compliance. The approach is validated through simulations demonstrating accurate posture tracking, effective disturbance rejection in rigid configurations, and controllable impedance under external loads, highlighting potential for prosthetics and humanoid robotics. The study advances the design of compact, compliant robotic wrists by integrating a nonlinear elastic transmission with a parallel architecture and an optimization-based stiffness controller.

Abstract

Variable Stiffness Actuators prove invaluable for robotics applications in unstructured environments, fostering safe interactions and enhancing task adaptability. Nevertheless, their mechanical design inevitably results in larger and heavier structures compared to classical rigid actuators. This paper introduces a novel 3 Degrees of Freedom (DoFs) parallel wrist that achieves variable stiffness through redundant elastic actuation. Leveraging its parallel architecture, the device employs only four motors, rendering it compact and lightweight. This characteristic makes it particularly well-suited for applications in prosthetics or humanoid robotics. The manuscript delves into the theoretical model of the device and proposes a sophisticated control strategy for independent regulation of joint position and stiffness. Furthermore, it validates the proposed controller through simulation, utilizing a comprehensive analysis of the system dynamics. The reported results affirm the ability of the device to achieve high accuracy and disturbance rejection in rigid configurations while minimizing interaction forces with its compliant behavior.

Figures (3)

• Figure 1: Representation of the device indicating its DoFs. In contrast to the human wrist, the Pronation/Supination motor solely rotates the end-effector rather than the entire forearm
• Figure 2: Schematic illustration depicting the kinematic configuration of the PM (a), a generic leg of the PM (b), and the PS transmission mechanism (c)
• Figure 3: Simulation results illustrating the wrist stiffness and motion behavior. a Cartesian compliance of the wrist in the central position across four distinct stiffness levels, juxtaposed with human wrist compliance $C_h$ extracted from Pando2014Wrist. b Corresponding elastic torque from the actuators. c Wrist motion behavior under loaded conditions, emphasizing the differences between the soft (LS, dashed lines) and rigid (HS, diamond lines) configurations. Continuous lines denote posture references. Blue lines indicate the FE angles, while red lines represent the RUD angles