Investigation of Parallel Manipulators Using Linear Complex Approximation

[+] Author and Article Information
A. Wolf, M. Shoham

Robotics Laboratory, Department of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel

J. Mech. Des 125(3), 564-572 (Sep 04, 2003) (9 pages) doi:10.1115/1.1582876 History: Received November 01, 2001; Revised November 01, 2002; Online September 04, 2003
Copyright © 2003 by ASME
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Grahic Jump Location
Gough-Stewart platform, the lines Li and the resulting twists
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(a) Hunt’s singularity—two limbs and the moving platform are coplanar; (b) λ as function of the moving, platform rotation angle, α, about the LCA axis of Fig. 2(a)
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(a) Fichter’s singularity—90 deg rotation of the moving platform about the Z axis, top views; (b) Fichter’s singularity—90 deg rotation of the moving platform, from home position, about the Z axis: isometric views; (c) λ as a function of the moving platform rotation angle about the Z axis. (d) Values of the closest linear complex’s pitch as a function of the moving platform rotation angle about the Z axis.
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The TSSM Manipulator, Merlet 17
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Type 3c singularity with four line-1,2,3,5-intersect at vertex B1
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(a) Type 4d singularity where lines LCA1 and LCA2 cross the plane spanned by L1 and L2, vertex B3 joining L5 and L6 and intersect a line along limb 4: top view; (b) Type 4d singularity (LCA2 not shown for clarity): side view.
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(a) A 3-DOF 3-UPU parallel manipulator 31; (b) A 3-DOF 3-UPU parallel manipulator (SNU)
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Equivalent kinematic structure of the UPU robot’s limb
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Force and moment transmitted to the moving platform
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3-UPU with two zero-pitch linear complexes
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The path of the moving platform on a sphere centered at IPL
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Points in the vicinity of the base configuration, on a sphere centered at IPL
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Minimum λ corresponding to two LCA in points of Fig. 12
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Maximum λ at each point of Fig. 12
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Two pitches corresponding to the two linear complexes with minimum λ at each point of Fig. 12
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Pitch of linear complex with max λ at each point of Fig. 12




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