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Research Papers

Actuation Torque Reduction in Parallel Robots Using Joint Compliance

[+] Author and Article Information
Júlia Borràs

Department of Mechanical Engineering
and Materials Science,
Yale University,
New Haven, CT 06520
e-mail: julia.borrassol@yale.edu

Aaron M. Dollar

Department of Mechanical Engineering
and Materials Science,
Yale University,
New Haven, CT 06520
e-mail: aaron.dollar@yale.edu

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received April 22, 2013; final manuscript received December 20, 2013; published online March 4, 2014. Assoc. Editor: Andreas Müller.

J. Mechanisms Robotics 6(2), 021006 (Mar 04, 2014) (11 pages) Paper No: JMR-13-1080; doi: 10.1115/1.4026628 History: Received April 22, 2013; Revised December 20, 2013

This work studies in detail how the judicial application of compliance in parallel manipulators can produce manipulators that require significantly lower actuator effort within a range of desired operating conditions. We propose a framework that uses the Jacobian matrices of redundant parallel manipulators to consider the influence of compliance both in parallel with the actuated joints as well as the passive joints, greatly simplifying previous approaches. We also propose a simple optimization procedure to maximize the motor force reduction for desired regions of the workspace and range of external forces. We then apply the method to a Stewart-Gough platform and to a 3-URS (universal rotational and spherical joint) manipulator. Our results show that parallel manipulators with tasks that involve a preferred external force direction, as for instance, big weights in the platform, can see large reductions in actuator effort through the judicial use of compliant joints without significantly losing rigidity.

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References

Figures

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Fig. 1

Classification of joints with and without compliance. In the parallel robot literature, any nonactuated joint is called passive, but as the passive compliant joint exerts a torque, we have to consider it as active for the static analysis.

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Fig. 2

Simple example of the combination of actuation torque exerted by the motor τm, compliant torque exerted by the spring τs, and reaction torque to the external force τf

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Fig. 6

Top: Each applied force is associated with a dot in a sphere. Bottom: The colors represent the percentage of the workspace with reduction (first column) or the net increase (second column) of the overall torque in the first row, or the maximum motor torque in the second row.

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Fig. 4

Workspace discretization. (a) Position workspace. The points represent a third of the workspace, with darker color when more orientations are achievable. Points inside the sphere are considered part of the central workspace. (b) Orientation workspace for the shown position. Each dot represents an orientation of the vector Lambda, that is perpendicular to the platform. The red arrows show an additional rotation around Lambda. All orientations of Lambda inside the cone showed are considered part of the central workspace.

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Fig. 5

(a) Top: Histogram of the percentage of increase/decrease of the motor force for each configuration in the workspace. Bottom representation of the position workspace, and a third of it. The colors represent the mean percentage of reduction for all the orientations achievable from each dot position. (b) Top: Comparison between histograms of the maximum torque values over the configurations of the workspace with and without compliant joints. Bottom: representation of the static workspace. Each dot color represents the median torque for all the possible orientations in the corresponding position of the dot. All points where the maximum force is bigger than 5 are discarded.

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Fig. 3

Stewart-Gough platform equivalent to the octahedral design (top) and its corresponding notation (bottom). See Table 1 for coordinates of vectors zi and wi.

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Fig. 8

Notation for the 3-URS manipulator

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Fig. 7

Percentages of reduction of the motor torque when changing the magnitude of the applied force. Each color corresponds to a different direction of applied force. Dashed (solid) lines are results of a manipulator using the compliant parameters in Eqs. (30) and (31).

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Fig. 11

Comparison of manipulators using the compliant parameters optimized for a range of forces of magnitude 10 N (Eq. (36)) and for a range of forces of magnitude 2 N.

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Fig. 12

Similarly to Fig. 6, each dot represents a direction of the external applied force, and its color the percentage of workspace with reduction (first column) and the net reduction (second column). Reductions of the overall torque are shown in the first row, while reductions of the maximum torque in each configuration are shown in the second row.

Grahic Jump Location
Fig. 9

Top: Histogram of the percentage of increase of the overall motor torque in each configuration of the workspace. Bottom: Each dot in the position workspace is colored depending on the mean reduction of the overall motor torque for all the orientations achievable from the dot position. From the left figure, (a) shows only a third to the figure, and (b) only the third and only configurations with reduction.

Grahic Jump Location
Fig. 10

Top: Comparison between histograms of the maximum torque values over the configurations of the workspace with and without compliant joints. Bottom: A representation of the static workspace. Each dot color represents the median torque for all the possible orientations in the corresponding position of the dot. All points where the maximum torque is bigger than 10 Nm are discarded.

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