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Research Papers

Kinematic and Dynamic Analysis of a Two-Degree-of-Freedom Spherical Wrist

[+] Author and Article Information
M. Ruggiu

Department of Mechanical Engineering, University of Cagliari, Piazza d’Armi, 09123 Cagliari, Italyruggiu@dimeca.unica.it

In particular the third specialization of the symmetrically actuated generalized double pointing system in Ref. 2 is similar to the wrist proposed here. As it is clear from Fig. 7 in Ref. 2, in this case, the center of the motion is precluded to the item to be scanned for the presence of one of the actuator axes. Moreover, the motivation of the work, the analysis conducted are fully independent and distinct.

Explicit expression for τ can be provided by the author upon request.

J. Mechanisms Robotics 2(3), 031006 (Jul 14, 2010) (10 pages) doi:10.1115/1.4001889 History: Received February 19, 2009; Revised January 15, 2010; Published July 14, 2010; Online July 14, 2010

The present paper proposes the analysis of a spherical wrist with two degrees of freedom for scanning system applications. The wrist consists of two chains of revolute-revolute pairs. A slotted arc connecting the two chains behaves as a further revolute pair. Thus, the mechanism is an overconstrained (meaning of this definition is discussed in this work) single-loop kinematic chain composed of five revolute pairs equivalent to a spherical motion generator since all its axes intersect at a point. Throughout the paper, the kinematic analysis is developed including some details about the workspace, which depends on the design of the slotted arc. The performance index given as the inverse of the condition number is used to measure the performances of the motion of the moving platform of the wrist. The singularity poses found were examined in detail. A simplified dynamic model is proposed that provides the torques suitable for satisfying a given kinematics. Finally, the paper presents a motorized hardware model of the mechanism assembled in the laboratory.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

The geometry of the wrist

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Figure 2

Reference frames in the kinematic analysis

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Figure 3

Design schemes of the slotted arc: (a) design I and (b) design II

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Figure 4

ϵ versus ϑ1 and ϑ2

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Figure 5

Workspace in the joint space: design II

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Figure 6

Workspace in the joint space: design I

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Figure 7

Cartesian workspace: design I

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Figure 8

Ψ and Θ: design I

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Figure 9

Ψ and Θ: design II

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Figure 10

ζ(J) versus ϑ1, ϑ2

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Figure 11

Singularity of type 1

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Figure 12

Singularity of type 2

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Figure 13

Trajectory of the reference point P in the numerical example

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Figure 14

ζ(J) versus ϑ1 and ϑ2 in the numerical example

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Figure 15

τ1 (●), τ2 (+)versus ϑ1 and ϑ2 in the numerical example

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Figure 16

Solid model of the orienting mechanism

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Figure 17

The hardware model of the orienting mechanism

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Figure 18

Frames captured during a test of motion

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