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Technical Briefs

Workspace Analysis of a Novel Six-Degrees-of-Freedom Parallel Manipulator With Coaxial Actuated Arms

[+] Author and Article Information
Mats Isaksson

e-mail: mats.isaksson@gmail.com

Matthew Watson

e-mail: matthew.g.watson@gmail.com
Centre for Intelligent Systems Research,
Deakin University,
75 Pigdons Road,
Waurn Ponds VIC 3216, Australia

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 30, 2012; final manuscript received May 8, 2013; published online July 18, 2013. Assoc. Editor: Chintien Huang.

J. Mech. Des 135(10), 104501 (Jul 18, 2013) (9 pages) Paper No: MD-12-1336; doi: 10.1115/1.4024723 History: Received June 30, 2012; Revised May 08, 2013

Parallel manipulators possess several advantages compared to serial robots, including the possibilities for high acceleration and high accuracy positioning of the manipulated platform. However, the majority of all proposed parallel mechanisms suffer from the combined drawbacks of a small positional workspace in relation to the manipulator footprint and a limited range of rotations of the manipulated platform. This paper analyses a recently proposed six-degrees-of-freedom parallel mechanism that aims to address both these issues while maintaining the traditional advantages of a parallel mechanism. The investigated manipulator consists of six actuated coaxial upper arms that are allowed to rotate indefinitely around a central cylindrical base column and a manipulated platform where five of the six joint positions are collinear. The axis-symmetric arm system leads to an extensive positional workspace while the proposed link arrangement increases the range of achievable platform rotations. The manipulator workspace is analyzed in detail and two methods to further increase the rotational workspace are presented. It is shown that the proposed manipulator has the possibility of a nonsingular transition of assembly modes, which extends the usable workspace. Furthermore, it is demonstrated how an additional kinematic chain can be utilized to achieve infinite platform rotation around one platform axis. By introducing additional mobility in the manipulated platform, a redundantly actuated mechanism is avoided.

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References

Figures

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Fig. 1

The Hexarot-5 manipulator. (a) Arms and joints, (b) coordinate systems and kinematic parameters, (c) one of the 3-DOF joints on the upper arms, and (d) three of the joints on the manipulated platform.

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Fig. 2

The joint angle qi for one upper arm Ai is determined from the upper arm length ai, the length  xyli of the lower arm link Li projected in the xy-plane and the position  xyPi of the platform joint Pi projected in the xy-plane.

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Fig. 3

Six configurations of a Hexarot-5 manipulator with the structural parameters in Table 1. In all six configurations, the origin of the coordinate system M (the joint axes intersection point of joint P1) is in the same position in the center of the radial workspace (11) while the platform orientation varies. In each plot the platform has been rotated around an axis that is parallel to a coordinate axis of F and intersects the origin of M. Starting from the platform orientation (12), the rotations have been increased until any limitation has been reached.

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Fig. 4

The plots show all reachable positions in the xz-plane (x > 0, y = 0) for a Hexarot-5 manipulator with the parameters in Table 1. In each position reachable with the orientation (12), the maximum possible rotation around an axis intersecting the origin of M in the direction of a coordinate axis of F, has been determined. In (a) and (d), these directions are the negative and positive x-axis of F, in (b) and (e), they are the negative and positive y-axis of F, while in (c) and (f) they are the negative and positive z-axis of F. If the maximum achievable rotation is less than 45 deg, the platform position is colored red; if it is between 45 deg and 60 deg, it is colored blue, while positions where a larger angle than 60 deg can be achieved are colored green. Different markers are used to show the limiting factor for further rotations in each position. The use of a triangle signifies a Type 2 singularity, a square signifies collision and a filled circle indicates that the inverse kinematics lacks a solution due to reach.

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Fig. 5

A cross-section (x > 0, y = 0) of the positional workspace for the Hexarot-5 manipulator with the parameters in Table 1. Each position is colored according to the maximum platform rotation that is achievable around all evaluated axes, starting from the platform orientation (12). If the achievable rotation angle is less than 45 deg, the platform position is colored red and if it is between 45 deg and 60 deg, it is colored blue. Different markers are used to show the limiting factor for further rotation in each position. The use of a triangle signifies a Type 2 singularity, a square signifies collision and a filled circle indicates that there is no solution due to reach.

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Fig. 6

Three variants of the Heptarot-5 manipulator utilizing a seventh actuated kinematic chain to achieve infinite rotation of the manipulated platform around the axis defined by the five collinear platform joints. (a) Redundantly actuated mechanism. (b) Kinematically redundant mechanism employing a parallelogram between two platform sections. (c) Kinematically redundant mechanism employing a linear bearing between two platform sections.

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Fig. 7

The values of the Jacobian determinants when moving from JSC 1O to JSC 2N. The thick blue line illustrates det(Jx) and the thin red line shows det(Jq)/100. The circles separate the five path segments. As can be seen, det(Jx) remains larger than zero during the entire path.

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