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Research Papers

Singularity Analysis of Large Workspace 3RRRS Parallel Mechanism Using Line Geometry and Linear Complex Approximation

[+] Author and Article Information
Alon Wolf

Biorobotics and Biomechanics Laboratory, Faculty of Mechanical Engineering, Technion-IIT, Haifa 32000, Israelalonw@technion.ac.il

Daniel Glozman

Biorobotics and Biomechanics Laboratory, Faculty of Mechanical Engineering, Technion-IIT, Haifa 32000, Israel

J. Mechanisms Robotics 3(1), 011004 (Nov 30, 2010) (9 pages) doi:10.1115/1.4002815 History: Received May 30, 2010; Revised September 22, 2010; Published November 30, 2010; Online November 30, 2010

During the last 15 years, parallel mechanisms (robots) have become more and more popular among the robotics and mechanism community. Research done in this field revealed the significant advantage of these mechanisms for several specific tasks, such as those that require high rigidity, low inertia of the mechanism, and/or high accuracy. Consequently, parallel mechanisms have been widely investigated in the last few years. There are tens of proposed structures for parallel mechanisms, with some capable of six degrees of freedom and some less (normally three degrees of freedom). One of the major drawbacks of parallel mechanisms is their relatively limited workspace and their behavior near or at singular configurations. In this paper, we analyze the kinematics of a new architecture for a six degrees of freedom parallel mechanism composed of three identical kinematic limbs: revolute-revolute-revolute-spherical. We solve the inverse and show the forward kinematics of the mechanism and then use the screw theory to develop the Jacobian matrix of the manipulator. We demonstrate how to use screw and line geometry tools for the singularity analysis of the mechanism. Both Jacobian matrices developed by using screw theory and static equilibrium equations are similar. Forward and inverse kinematic solutions are given and solved, and the singularity map of the mechanism was generated. We then demonstrate and analyze three representative singular configurations of the mechanism. Finally, we generate the singularity-free workspace of the mechanism.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

RRRS manipulator

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Figure 2

Kinematic architecture and design parameters of RRRS manipulator

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Figure 3

Manipulator folded to a plane

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Figure 4

The kinematics chain i of RRRS robot: Ŝ1,i∥Ŝ2,i∥Ŝ3,i∥Ŝ6,i⊥Ŝ4,i⊥Ŝ5,i

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Figure 5

3D plot of the singularity map of the manipulator in C-space (left). Cut section view of the singularity map (right), base ring of the robot is plotted in blue.

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Figure 6

Cut section of the singularity map in Fig. 5. The singular point investigated is denoted by X. (Case 1: Linear complex).

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Figure 7

Manipulator in the singular configuration. Linear complex axis is in green.

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Figure 8

Cut section of the singularity map in Fig. 5. Singular point investigated is denoted by X. (Case 2: Hyperbolic congruence).

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Figure 9

Manipulator in the singular configuration. Linear congruence axes are in green (3D and side views).

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Figure 10

Cut section of the singularity map in Fig. 5. Singular point investigated is denoted by X. (Case 3: Plane).

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Figure 11

Manipulator in the singular configuration. Linear congruence axes are in green.

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Figure 12

Condition number map of the manipulator

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Figure 13

Nonsingular workspace of the manipulator with transparent singular workspace (red ring is the robot base platform)

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