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RESEARCH PAPERS

Type Synthesis of 3-DOF PPR-Equivalent Parallel Manipulators Based on Screw Theory and the Concept of Virtual Chain

[+] Author and Article Information
Xianwen Kong

Département de Génie Mécanique, Université Laval, Québec, Québec, Canada, G1K 7P4xwkong@gmc.ulaval.ca

Clément M. Gosselin2

Département de Génie Mécanique, Université Laval, Québec, Québec, Canada, G1K 7P4gosselin@gmc.ulaval.ca

2

Corresponding author.

J. Mech. Des 127(6), 1113-1121 (Mar 16, 2005) (9 pages) doi:10.1115/1.2044787 History: Received June 30, 2004; Revised March 16, 2005

PPR-equivalent parallel manipulators (PMs) are a class of 3-DOF PMs with great application potential. They are indeed the parallel counterparts of the 3-DOF PPR serial robots, in which the moving platform can rotate arbitrarily about an axis undergoing a planar translation. This paper deals with the type synthesis of 3-DOF PPR-equivalent PMs. At first, virtual chains are introduced to represent the motion patterns of 3-DOF motions and relevant results from screw theory are recalled. A method is then proposed for the type synthesis of 3-DOF PPR-equivalent PMs. Using the proposed approach, the type synthesis of 3-DOF PPR-equivalent PMs is performed in three steps. In addition to all the 3-DOF PPR-equivalent parallel kinematic chains and 3-DOF PPR-equivalent PMs proposed in the literature, a number of new 3-DOF PPR-equivalent parallel kinematic chains and 3-DOF PPR-equivalent PMs are identified. It is also found that there are no PPR-equivalent PMs with identical type of legs. The type synthesis of PPR-equivalent PMs is well solved using the proposed approach. The characteristic of the proposed approach is that the type synthesis of PPR-equivalent parallel kinematic chains is reduced to the type synthesis of 3-DOF single-loop kinematic chains and thus easy to perform.

Copyright © 2005 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

PPR virtual chain

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Figure 3

(a) Three-legged PPR-equivalent parallel kinematic chain; (b) Three-legged PPR-equivalent parallel kinematic chain with a PPR virtual chain added

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Figure 4

PPR virtual chain

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Figure 5

Leg-wrench systems of PPR-equivalent parallel kinematic chains

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Figure 6

Serial kinematic chains

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Figure 7

Some 3-DOF single-loop kinematic chains involving a PPR virtual chain

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Figure 8

Some legs for PPR-equivalent parallel kinematic chains

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Figure 9

(a) 2-(RRR)NRa-RA(RRR)BRA PPR-equivalent parallel kinematic chain with a PPR virtual chain added; (b) 2-(RRR)NRa-RA(RRR)BRA PPR-equivalent parallel kinematic chain

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Figure 10

2-(RRR)NRa-(RR)B(RRR)A PPR-equivalent parallel kinematic chain

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Figure 11

3-(PP)NRa PPR-equivalent parallel kinematic chains

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Figure 12

Some possible PPR-equivalent parallel manipulators: (a) 2-(ṞRR)NRa-(ṞR)B(RRR)A, (b) 2-(ṞRR)NRa-ṞA(RRR)BRA

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Figure 13

Actuation wrenches of some legs for PPR-equivalent parallel kinematic chains

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Figure 14

Some 3-DOF PPR-equivalent PMs of family 3: (a) 2-(ṞRR)NRa-ṞA(RR)BRARA, and (b) 2-(RP̱R)NRa-RA(RP̱R)BRA

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Figure 15

Some 3-DOF PPR-equivalent PMs of family 13: (a) 2-(ṞRR)N(RR)I-ṞA(RRR)BRA, and (b) 2-(ṞR)N(RRR)I-ṞA(RRR)BRA

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Figure 16

Some 3-DOF PPR-equivalent PMs of family 2: (a) 2-(ṞRR)NRa-(ṞRPR)A, and (b) 2-(P̱RR)NRa-(P̱RPR)A

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Figure 17

2-RP̱U-UP̱U PPR-equivalent PMs

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