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Research Papers

Orientation Workspace and Stiffness Optimization of Cable-Driven Parallel Manipulators With Base Mobility

[+] Author and Article Information
Michael Anson

Mechanical and Aerospace Engineering,
SUNY at Buffalo,
Buffalo, NY 14260
e-mail: mjanson@buffalo.edu

Aliakbar Alamdari

Mechanical and Aerospace Engineering,
SUNY at Buffalo,
Buffalo, NY 14260
e-mail: aalamdar@buffalo.edu

Venkat Krovi

Professor
Fellow ASME
Mechanical and Aerospace Engineering,
SUNY at Buffalo,
Buffalo, NY 14260
e-mail: vkrovi@buffalo.edu

1Corresponding author.

Manuscript received July 7, 2016; final manuscript received January 31, 2017; published online March 23, 2017. Assoc. Editor: Byung-Ju Yi.

J. Mechanisms Robotics 9(3), 031011 (Mar 23, 2017) (16 pages) Paper No: JMR-16-1196; doi: 10.1115/1.4035988 History: Received July 07, 2016; Revised January 31, 2017

Cable-driven parallel manipulators (CDPM) potentially offer many advantages over serial manipulators, including greater structural rigidity, greater accuracy, and higher payload-to-weight ratios. However, CDPMs possess limited moment resisting/exerting capabilities and relatively small orientation workspaces. Various methods have been contemplated for overcoming these limitations, each with its own advantages and disadvantages. The focus of this paper is on one such method: the addition of base mobility to the system. Such base mobility gives rise to kinematic redundancy, which needs to be resolved carefully in order to control the system. However, this redundancy can also be exploited in order to optimize some secondary criteria, e.g., maximizing the size and quality of the wrench-closure workspace with the addition of base mobility. In this work, the quality of the wrench-closure workspace is examined using a tension-factor index. Two planar mobile base configurations are investigated, and their results are compared with a traditional fixed-base system. In the rectangular configuration, each base is constrained to move along its own linear rail, with each rail forming right angles with the two adjacent rails. In the circular configuration, the bases are constrained to move along one circular rail. While a rectangular configuration enhances the size and quality of the orientation workspace in a particular rotational direction, the circular configuration allows for the platform to obtain any position and orientation within the boundary of the base circle. Furthermore, if the bases are configured in such a way that the cables are fully symmetric with respect to the platform, a maximum possible tension-factor of one is guaranteed. This fully symmetric configuration is shown to offer a variety of additional advantages: it eliminates the need to perform computationally expensive nonlinear optimization by providing a closed-form solution to the inverse kinematics problem, and it results in a convergence between kinematic singularities and wrench-closure singularities of the system. Finally, we discuss a particular limitation of this fully symmetric configuration: the inability of the cables to obtain an even tension distribution in a loaded configuration. For this reason, it may be useful to relax the fully symmetric cable requirement in order to yield reasonable tensions of equal magnitude.

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Figures

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Fig. 1

Virtually prototyping cable-driven parallel manipulators with base mobility in multi-domain modeling and simulation tools

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Fig. 2

(a) Rectangular base configuration and (b) circular base configuration

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Fig. 3

(a) Kinematic singularities in the fixed-base system, architecture singularity, (b) kinematic singularities in the fixed-base system, type I singularity, (c) type I singularities in systems with rectangular base mobility, (d) type I singularities in systems with circular base mobility, and (e) type III kinematic singularity in the circular base configuration

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Fig. 4

(a)–(c) Common type II kinematic singularities in the rectangular base configuration (d)–(f) common type II kinematic singularities in the circular base configuration

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Fig. 5

Example wrench-closure workspace and tension factor map for fixed-base system

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Fig. 6

(a) Example internal wrench-closure singularities in the fixed configuration, (b) example internal wrench-closure singularities in the rectangular base configuration, and (c) example internal wrench-closure singularities in the circular base configuration

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Fig. 7

Approaching the boundary: (a) and (b) fixed-base, (c) and (d) rectangular configuration, (e) and (f) circular configuration

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Fig. 8

Orientation workspace: (a) fixed-base, (b) rectangular configuration, and (c) circular configuration

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Fig. 9

Wrench-closure orientation workspace at x = 0, y = 0: (a) fixed-base, (b) rectangular configuration, and (c) circular configuration

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Fig. 10

Position control scheme for trajectory tracking

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Fig. 11

Graphical user interface (GUI)

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Fig. 12

Trajectory tracking results: (a) rectangular configuration and (b) circular configuration

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Fig. 13

Relative angle limits

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Fig. 14

Eigenvalue and objective function results for sample system

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Fig. 15

Effect of platform dimensions on optimal relative angle

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Fig. 16

(a) and (b) Optimal relative angle for sample trajectory

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Fig. 17

Unit force applied in x-direction of platform frame

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Fig. 18

(a) Tension requirements to evenly balance Fx, (b) tension requirements to evenly balance Fy, and (c) tension requirements to evenly balance Mz

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