Elsevier

Mechanism and Machine Theory

Volume 116, October 2017, Pages 34-49
Mechanism and Machine Theory

Research paper
Principle of operation of RotWWC-VSA, a multi-turn rotational variable stiffness actuator

https://doi.org/10.1016/j.mechmachtheory.2017.05.006Get rights and content

Highlights

  • The principle of operation of the RotWWC-VSA is presented.

  • RotWWC-VSA is a multi-turn rotational variable stiffness actuator.

  • The equations to analyze the mechanism are presented.

  • Simulation results are given and commented.

  • The concept design of a prototype embedding the RotWWC-VSA is described.

Abstract

This work presents the principle of operation of RotWWC-VSA, a Variable Stiffness Actuator (VSA) characterized by no rotational stroke limits, conversely to the vast majority of rotational VSAs, typically characterized by restrictions in the angular range of motion. The possibility to perform an unlimited number of turns is a characteristic taken for granted for standard motors, but it is not for VSA rotational motors. It features two antagonist nonlinear equivalent springs, each of them made up of a tension spring, a cam and a wire which, properly configured, realize a torsion spring characterized by a customizable non-linear stiffness characteristic. Theoretical aspects of the actuator are accompanied by numerical simulations. Design guidelines are drawn and a concept design is presented.

Introduction

A Variable Impedance Actuator (VIA) is an actuator which deviates from its set equilibrium position, depending on the external forces and the mechanical properties of the actuator (i.e. inertia, stiffness and damping factors), oppositely to non-VIA (traditional stiff actuator) characterized by excellent trajectory tracking with a high bandwidth and high accuracy [1]. Inherent compliant actuators constitute a subgroup of VIAs, containing a passive or intrinsic compliant element in series to the (stiff) actuator. They can be subdivided into Series Elastic Actuators (SEA - Fig. 1a) [2], in which the compliant element does not change its stiffness (fixed compliance), and Variable Stiffness Actuators (VSA - Fig. 1b) [3], in which the stiffness is controlled by mechanical reconfiguration.

VSAs [1] allow the adjustment, in a controlled manner and at the same time, of both the mechanical stiffness and the equilibrium configuration of the load. Peculiar features are mechanical stiffness adjustment, adaptability and force accuracy in the interaction with the operator facilitating a direct interaction with humans limiting forces in case of collision, and robustness to external perturbations or model errors [4]. All of them are obtained without necessarily requiring force-based control techniques, favoring mechanical backdrivability, transparency and bandwidth.

For all these aspects, potentially positive in a number of applications, a number of different VSAs have been recently conceived and realized [1], [5], [6]. Moreover, the more and more growing interest in VSAs led Grioli et al. to present a VSA datasheet as an interface language between designers and users and to discuss design procedures and how VSA data may be organized to minimize the engineer’s effort in choosing the actuator type and size [7]. In order to further support designers in developing new VSA solutions, design guidelines for R&D engineers facing the challenge of designing new VSA systems and implementing them in use-cases as shock absorbing, stiffness variation, cyclic motions and explosive motions are proposed [6].

It is a matter of fact that the vast majority of the so-far developed VSAs perform rotational motions. Nevertheless, if compared to traditional rotational actuators which typically can perform bidirectionally an infinite number of turns, the majority of rotational VSAs are characterized by restrictions in the actually exploitable range of motion. In fact, to the authors’ knowledge, only few rotational VSAs have so far being developed featuring an infinite number of turns. Among them it is worth to mention the PVSA [8], the actuator developed by Tonietti et al. [9] and the ComPact-VSA [10]. However, all of them requires a great number of manufactured parts. Moreover, the first two of them are characterized by the presence of a pin-slot joint which requires precise manufacturing and assembling operations. The vsaUT-II [11] guarantees a large variation of stiffness but requires many manufactured components and mechanical joints as gears and pin-slot joints. Moreover, it is affected by a limited rotational range of motion. The use of profiled surfaces is considered promising to customize the stiffness-displacement curve. Both the VS-Joint mechanism [12] and the third architecture presented by Guo et al. in [13] require a pin-slot joint and good mechanical tolerances. Similar and alternative solutions are presented in [14]. Interesting is AMASC [15] which adopts coupled cams to obtain springs non-linearity.

In order to realize linear motions using rotational actuators, it is common the use of mechanical transmissions based on rack and pinion, pulley and belt, or drum and wire. However, with the purpose of realizing linear actuators with (theoretically) no stroke restrictions, the employed actuators require not to be affected by any rotational limit or end stroke (i.e. they should be able to perform an unlimited number of turns). Summarizing, few rotational VSAs can be effectively exploited for this aim. Moreover, the existing ones are typically characterized by a great number of components and require strict-tolerance machining and assembling operations to avoid backlashes or jammings.

An interesting solution for the aims of this work is the LinWWC-VSA, proposed by Spagnuolo et al. [16], a VSA architecture designed to perform linear motions with a theoretically infinite stroke. It features two antagonistic SEAs, each of them made up of a cam wrapped by a wire and constrained by a torsion spring. Taking inspiration from its principle of operation, the Rotational Wire-Wrapped Cam VSA (RotWWC-VSA) has been conceived. It is an Agonist-Antagonist VSA (AAVSA) [3], [4] suitable to actuate rotational axes with no restrictions in the actually exploitable range of motion, able to perform an unlimited number of turns. It is made up of two antagonistic RotWWC-SEA, each of them featuring a tension spring, a cam and a wire which, properly configured, realize a torsion spring characterized by a customizable non-linear stiffness characteristic.

The use of a cam wrapped by a wire is considered promising in order to minimize the number of mechanical components, as better described in next sections, simplifying the design and assembly operations, and limiting concentrated mechanical stresses. Examples of employment of this approach are the MACCEPA 2.0 [17], the pnrVSA [18], the one proposed by Shin et al. actuated by pneumatic artificial muscles [19], the NLSs proposed by Schepelmann et al. [20], and the mechanism described in [21]. However, all of them are configured to perform rotational movements characterized by a limited rotational range of motion, conversely to the RotWWC-VSA.

Within the present work, the principle of operation and the analysis of the RotWWC-VSA actuator is presented. It is a mechanism dual with respect to the LinWWC-VSA mechanism presented in [16]. Despite some similarities and some common elements, the mechanism described within this new paper faces a completely different actuation setup and application scenario. While LinWWC-VSA has been conceived to realize an intrinsic variable-stiffness linear actuator embedding the non-linear adjustable stiffness within a linear carriage, RotWWC-VSA realizes a multi-turn VSA. With respect to other rotational VSAs it is multi-turn, characteristic which is not widespread among rotational VSAs, and realized with relatively simple components without requiring precise manufacturing and assembling operations, as some others previously described. Within this paper, aspects already faced in [16], as numerical and analytical methods to design the cam embedded within the actuator, will not be described in details and will be referenced to.

The work is organized as follows. The list of used symbols is reported in Table 1. A list of nomenclature is reported in Table 2. General aspects about AAVSA are summarized in Section 2. The RotWWC-SEA is analyzed in Section 3. The RotWWC-VSA is illustrated in Section 4. Simulations and related discussions are reported in Section 5. Design guidelines are presented in Section 6. The concept design of a RotWWC-VSA -based actuator is shown in Section 7. Conclusions and future works are drawn in Section 8.

Section snippets

General aspects of Agonist-Antagonist VSAs

An Agonist-Antagonist VSA (AAVSA) mimics the principle at the basis of antagonist muscles [22], for which the stronger the antagonistic forces are, the stiffer the articulation becomes [5]. It is made up of two antagonist SEAs, kinematically in parallel with respect to a mobile mass (Fig. 2). The non-linearity of the elastic element is required to allow the adjustment of the VSA stiffness [4].

Referring to Fig. 1 let us denote by a a generic compliant rotational actuator made up of a rigid joint

RotWWC-SEA

Referring to Fig. 4, let us consider a cam defined by the curve c(r, θ) wrt the reference frame {c}. Let us conveniently consider a cam shaped as a spiral, with r monotonically increasing wrt θ. Let us denote by A(rA, θA) and B(rB, θB) the points of the cam with the minimum and maximum values of r, respectively. It is rArrB and θAθθB. Considering a point Tc, let us denote by t the line passing through T and tangent to c, and by H the point on t at minimum distance b from Oc.

As it

RotWWC-VSA

Applying the principle of operation depicted in Fig. 2, it is possible to configure two antagonistic RotWWC-SEA s to realize a RotWWC-VSA. The RotWWC-SEA has been represented in Section 3, assuming the cam as fixed with respect to the absolute frame of reference and the free endpoint of the wire E rotating about the center of the cam. Oppositely, let us hereafter consider two cams c1 and c2 rigidly constrained to an inertia I which can rotate around the axis z, as depicted in Fig. 7. For

Analysis of the RotWWC-VSA and discussion

Let us now consider a numerical example to better analyze the principle of operation of the actuator, considering a RotWWC-VSA made up of two antagonist RotWWC-SEA featuring logarithmic spirals. As explained in [16], the logarithmic spiral is beneficial from the design point of view, since it allows an analytic definition of the cam profile on the basis of convenient parameters from an engineering point of view. In particular, as detailed in [16], in order to realize a non-linear spring

Design guidelines

The description of the mechanism, the analysis and the discussion carried out in previous sections lead to draw some general guidelines to design actuators based on the architecture described within this paper.

Γkl is function of the minimum and maximum distances and of the tangent t to the cam profile. Therefore, given Γkl, in order to reduce the overall dimensions of the cam, it is beneficial to minimize the minimum radius of the cam rA, given a certain β. This also leads to reduce the maximum

Concept design of a RotWWC-SEA-based actuator

The concept design of an actuator embedding the RotWWC-VSA architecture is presented in Fig. 14. It features two input shafts si, actuated by two external and generic stiff motors, and one output shaft so, connected to the so-far described mechanism and characterized by a variable rotational stiffness.

The concept design of the mechanism which realizes a RotWWC-SEA (Fig. 6) is reported in Fig. 14a. Each input shaft si makes E, which is one of the endpoints of each spring kl, to rotate around O.

Conclusions

The RotWWC-VSA is an agonist-antagonist variable stiffness actuation scheme specifically conceived for realizing rotational actuators performing an infinite number of turns. RotWWC-VSA is a rotational VSA made up, similarly to LinWWC-VSA [16], of two spiral-shaped antagonist cams, each of them wrapped by a wire. As opposed to LinWWC-VSA, the cams are rigidly constrained to the output rotational axis of the actuator, the compliant element (a linear tension spring) has its endpoints constrained

Acknowledgments

This work was partially supported by the Italian private non-profit Cariplo Foundation within the BRIDGE project - Behavioural Reaching Interfaces during Daily antiGravity Activities through upper limb Exoskeleton.

The authors would like to thank João Carlos Dalberto and Roberto Bozzi for the support to the mechanical design and the realization of the actuator developed within the BRIDGE project, embedding the principle of operation of RotWWC-VSA.

References (22)

  • B. Vanderborght et al.

    Variable impedance actuators: a review

    Rob. Auton. Syst

    (2013)
  • G. Spagnuolo et al.

    Analysis and synthesis of linWWC-VSA, a variable stiffness actuator for linear motion

    Mech. Mach. Theory

    (2017)
  • N. Hogan

    Adaptive control of mechanical impedance by coactivation of antagonist muscles

    Autom. Control, IEEE Trans.

    (1984)
  • G. Pratt et al.

    Series elastic actuators

    Intelligent Robots and Systems 95. ’Human Robot Interaction and Cooperative Robots’, Proceedings. 1995 IEEE/RSJ International Conference on

    (1995)
  • K. Laurin-Kovitz et al.

    Design of components for programmable passive impedance

    Robotics and Automation, 1991. Proceedings., 1991 IEEE International Conference on

    (1991)
  • A. Jafari

    Coupling between the output force and stiffness in different variable stiffness actuators

    Actuators

    (2014)
  • R. Ham et al.

    Compliant actuator designs

    Rob. Autom. Mag., IEEE

    (2009)
  • S. Wolf et al.

    Variable stiffness actuators: review on design and components

    IEEE/ASME Trans. Mechatron.

    (2016)
  • G. Grioli et al.

    Variable stiffness actuators: the user’s point of view

    Int. J. Rob. Res.

    (2015)
  • K.-H. Nam et al.

    Compliant actuation of parallel-type variable stiffness actuator based on antagonistic actuation

    J. Mech. Sci. Technol.

    (2010)
  • G. Tonietti et al.

    Design and control of a variable stiffness actuator for safe and fast physical human/robot interaction

    Robotics and Automation, 2005. ICRA 2005. Proceedings of the 2005 IEEE International Conference on

    (2005)
  • Cited by (27)

    • Configuration synthesis of variable stiffness mechanisms based on guide-bar mechanisms with length-adjustable links

      2021, Mechanism and Machine Theory
      Citation Excerpt :

      According to the motor layout, VSAs can be simply classified into two categories: antagonistic-configuration VSAs and serial-configuration VSAs [7]. Bioinspired by human muscle actuation, antagonistic-configuration VSAs consist of two motors (each one in series with a nonlinear spring) mounted in an antagonistic manner to control the equilibrium position (a position where no external force is applied) and the actuator stiffness simultaneously [8–10]. However, antagonistic-configuration VSAs suffer from limitations in energy efficiency and control complexity.

    • Variable stiffness ankle actuator for use in robotic-assisted walking: Control strategy and experimental characterization

      2019, Mechanism and Machine Theory
      Citation Excerpt :

      The interest in VSAs in the fields of assistive and rehabilitation robotics is due to their potential to fill the gap between the conventional stiff actuators and the adaptable compliance of biological systems. As compared to conventional stiff actuators, VSAs have favorable characteristics such as the ability to minimize large forces due to shocks, the energy-efficiency due to their capability to store and release energy, the robustness to external perturbations or unpredictable model errors, and their versatility [27,34,35,37,38]. Furthermore, the adjustable compliance of VSAs is of great interest in circumstances in which the robots have to interact with humans or with an unknown environment to achieve a safer and more natural interaction between the robot and the user and/or the environment [27,34,35,37,38].

    View all citing articles on Scopus
    View full text