| Volume 21 Issue 09 - Publication Date: 1 September 2002 |
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| Kinematics and Singularity Analysis
of a Novel Type of 3-CRR 3-DOF Translational Parallel Manipulator
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| Xianwen Kong and Clément
M. Gosselin Département de Génie Mécanique
Université Laval Québec, Québec, Canada, G1K 7P4
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| A new three-degrees-of-freedom
(3-DOF) translational parallel manipulator (TPM) with linear actuators,
i.e., 3-CRR TPM, is first proposed. The rotation singularity analysis, the
inverse kinematics, the forward kinematics, and the kinematic singularity
analysis of the 3-CRR TPM are then performed. The analysis shows that the
proposed TPM has the following kinematic merits over previous TPMs. (1)
The forward displacement analysis can be performed by solving a set of linear
equations. (2) The Jacobian matrix of the TPM is constant. The inverse of
the Jacobian matrix can be pre-calculated, and there is no need to calculate
repeatedly the inverse of the Jacobian matrix in performing the forward
displacement analysis and forward velocity analysis. (3) There is no rotation
singularity. (4) There is no uncertainty singularity. (5) The TPM has a
fewer number of links or joints. The geometric condition for a 3-CRR TPM
to be isotropic is also revealed. Two additional kinematic merits exist
for the isotropic 3-CRR TPM. The first is that an isotropic 3-CRR TPM is
isotropic in its whole workspace. The second is that no calculation is needed
in order to pre-determine the inverse of the Jacobian matrix. Finally, preliminary
design considerations are presented. |
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| Multimedia Key |
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= Code |
= Image |
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Extension |
Type |
Description |
1 |
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Example
1 - Schematic description of the 3-CRR TPM |
2 |
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Example
2a - The isotropic 3-CRR TPM; CAD Model |
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Example
2b - The isotropic
3-CRR TPM; Plastic Model |
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Example
3 - The maximal workspace of the isotropic 3_CRR TPM |
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Example
4a - Some variations of the 3-CRR TPM; The 3-PRRR TPM |
6 |
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Example
4b - Some variations of the 3-CRR TPM; The 3-CRRR TPM |
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Example
5a - Some isotropic variations of the 3-CRR TPM; An isotropic
3-PRRR TPM |
8 |
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Example
5b - Some isotropic variations of the 3-CRR TPM; An isotropic
3-CRRR TPM |
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