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Research Papers

Directional Stiffness Modulation of Parallel Robots With Kinematic Redundancy and Variable Stiffness Joints

[+] Author and Article Information
Andrew L. Orekhov

Department of Mechanical Engineering,
Vanderbilt University,
Nashville, TN 37235
e-mail: andrew.orekhov@vanderbilt.edu

Nabil Simaan

Department of Mechanical Engineering,
Vanderbilt University,
Nashville, TN 37235
e-mail: nabil.simaan@vanderbilt.edu

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received July 2, 2018; final manuscript received April 26, 2019; published online July 8, 2019. Assoc. Editor: Shaoping Bai.

J. Mechanisms Robotics 11(5), 051003 (Jul 08, 2019) (9 pages) Paper No: JMR-18-1197; doi: 10.1115/1.4043685 History: Received July 02, 2018; Accepted April 26, 2019

Parallel robots have been primarily investigated as potential mechanisms with stiffness modulation capabilities through the use of actuation redundancy to change internal preload. This paper investigates real-time stiffness modulation through the combined use of kinematic redundancy and variable stiffness actuators. A known notion of directional stiffness is used to guide the real-time geometric reconfiguration of a parallel robot and command changes in joint-level stiffness. A weighted gradient-projection redundancy resolution approach is demonstrated for resolving kinematic redundancy while satisfying the desired directional stiffness and avoiding singularity and collision between the legs of a Gough/Stewart parallel robot with movable anchor points at its base and with variable stiffness actuators. A simulation study is carried out to delineate the effects of using kinematic redundancy with or without the use of variable stiffness actuators. In addition, modulation of the entire stiffness matrix is demonstrated as an extension of the approach for modulating directional stiffness.

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Figures

Grahic Jump Location
Fig. 1

A Stewart–Gough type parallel manipulator with kinematic redundancy introduced through movable base anchor points

Grahic Jump Location
Fig. 2

Geometry of robot used in kinematic simulations

Grahic Jump Location
Fig. 3

Directional stiffness along x, y, and z directions while following the spiral in Eq. (36). (a) Fixed anchor points with constant joint stiffness, (b) fixed anchor points with variable joint stiffness, (c) using kinematic redundancy with constant joint stiffness, and (d) using both kinematic redundancy and variable joint stiffness.

Grahic Jump Location
Fig. 4

(a) Configuration in which the desired spatial stiffness was computed, (b) initial configuration, and (c) final configuration after optimizing the base anchor locations to satisfy the spatial stiffness. Note that the configuration in (c) matches well with its counterpart in (a).

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