Design, Development and Scaling Analysis of a Variable Stiffness Magnetic Torsion Spring

Abstract

In this paper we report on the design, modeling, experimental testing and scaling analysis of a novel MAgnetic Variable stiffnEess spRIng-Clutch (MAVERIC) device, which may be used as the elastic element of Variable Stiffness Actuators (VSAs). The device, comprising two co-axial diametrically magnetized hollow cylinders, has two degrees of freedom: a rotation of the two cylinders around the common axis and a relative translation along the same axis. For small rotations, the torque arising from the magnetic interaction of the two cylinders is almost linearly proportional to their relative rotation, as in mechanical torsion springs. In addition, the stiffness of the equivalent spring can be varied continuously from a maximum value down to exactly zero by changing the axial overlap of the two cylinders. In this way the proposed device can be used both as a clutch (i.e., perfectly compliant element) and as a variable stiffness torsion spring. A prototype, designed after magnetostatic FEM simulations, has been built and experimentally characterized. The developed MAVERIC has an experimentally determined maximum transmissible torque of 109.81 mN m, while the calculated maximum stiffness is 110.2 mN m rad −1 . The amplitude of the torque-angle characteristic can be tuned linearly with a sensitivity of 12.63 mN m mm −1 rad −1 . Further simulations have been computed parameterizing the geometry and the number of pole pairs of the magnets.The maximum torque density reached for one pole pair is 47.21 · 10 3 N m m −3 , whereas for a fixed geometry similar to that of the developed prototype, the maximum torque is reached for seven pole pairs. Overall, compared to mechanical springs, MAVERIC has no fatigue or overloading issues. Compared to other magnetic couplers, torsion stiffness can be varied continuously from a maximum value down to exactly zero, when the device acts as a disengaged clutch, disconnecting the load from the actuator.

Conceptual Design and Analysis of Four Types of Variable Stiffness Actuators Based on Spring Pretension

“…The characteristic of a purely quadratic torsion spring is defined by τ(θ)=aθ 2 . From the principle of virtual work:…”

“…To achieve a prescribed load-displacement function (i.e., the purely quadratic spring F(L)= aL 2 ), the error function ΔF and ΔK are defined as:…”

“…Each compression spring is equipped with two linear bearings (4) and two guide shafts (1). The spring is placed in the pedestal (2), and the cam (3) is used to drive the roller. The pressure angle is an important parameter for evaluating the friction dissipation, and the range of angular deflection is an important measure of compliance.…”

“…Since classical stiff actuators lack adaptability, energy efficiency and interaction safety, compliant actuators are strongly recommended when robots coexist with human beings or physically interact with them [1,2]. Among the compliant actuators, the requirement of mechanically variable stiffness joints is fulfilled by a new generation of actuators called VSAs.…”

“…The optimal criteria of the VSA are elaborated as follows: (1) Stiffness should be changed without energy consumption. (2) Energy efficiency of stiffness adjustment should be 100%. (3) No energy should be required to maintain the stiffness.…”