Profile Synthesis of Planar Rotational–Translational Variable Joints

Brian J. Slaboch; Philip A. Voglewede

doi:10.1115/1.4027700

Journal of Mechanisms and Robotics | Volume 6 | Issue 4 | research-article

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Research Papers

Profile Synthesis of Planar Rotational–Translational Variable Joints

Brian J. Slaboch and Philip A. Voglewede ¹

[+] Author and Article Information

Brian J. Slaboch

Department of Mechanical Engineering,
Marquette University,
Milwaukee, WI 53233
e-mail: Brian.Slaboch@marquette.edu

Philip A. Voglewede

Department of Mechanical Engineering,
Marquette University,
Milwaukee, WI 53233
e-mail: Philip.Voglewede@marquette.edu

Nominal refers to the general shape of a joint, but not necessarily the final shape given that it may need to be modified to account for clearance or friction.

Note that R_uP_v variable joints are kinematically equivalent to P_vR_u variable joints.

Tolerances are ignored because there has been much work done by Sacks and Joskowicz [12] on the tolerance analysis of higher pairs. The focus of this work is purely on the kinematic analysis.

The profile of link 2 is considered to be a set of points as opposed to the lines and arcs that define link 1. It should also be noted that the points are rigidly connected to form the joint profile.

ϒ₁ is not placed in the table because it is used for every joint.

¹Corresponding author.

²The term “reconfigurable mechanism” should not be confused with self-reconfigurable robots which are not the focus of this work.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received August 22, 2012; final manuscript received January 14, 2014; published online July 2, 2014. Assoc. Editor: Jian S. Dai.

J. Mechanisms Robotics 6(4), 041012 (Jul 02, 2014) (9 pages) Paper No: JMR-12-1124; doi: 10.1115/1.4027700 History: Received August 22, 2012; Revised January 14, 2014

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Abstract

This paper presents an approach to the profile synthesis of planar, variable joints by combining higher variable joints. The possible permutations of planar, variable joints that change from a rotational to translational motion will be enumerated. A method will be provided to determine the profiles of variable joints, and a practical example will be presented to illustrate the proposed method.

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References

Kuo, C.-H., and Yan, H.-S., 2007, “On the Mobility and Configuration Singularity of Mechanisms With Variable Topologies,” ASME J. Mech. Des., 129(6), pp. 617–624. [CrossRef]

Dai, J., and Jones, J. R., 1998, “Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds,” 25th ASME Biennial Mechanisms and Robotics Conference, Atlanta, GA, September 13–16, ASME Paper No. DETC98/MECH-5902.

Kuo, C., 2004, “Structural Characteristics of Mechanisms With Variable Topologies Taking Into Account the Configuration Singularity,” Master's thesis, Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan.

Zhang, K., Dai, J. S., and Fang, Y., 2010, “Topology and Constraint Analysis of Phase Change in the Metamorphic Chanin and Its Evolved Mechanism,” ASME J. Mech. Des., 132(6), p. 121001. [CrossRef]

Gan, D., Dai, J., and Liao, Q., 2009, “Mobility Change in Two Types of Metamorphic Parallel Mechanisms,” ASME J. Mech. Rob., 1(4), p. 041007. [CrossRef]

Yan, H.-S., and Kuo, C.-H., 2006, “Representations and Identifications of Structural and Motion State Characteristics of Mechanisms With Variable Topologies,” Trans. Can. Soc. Mech. Eng., 30(1), pp. 19–40.

Wohlhart, K., 1996, “Kinematotropic Linkages,” Recent Advances in Robot Kinematics, J.Lenarcic, and V.Parenti-Castelli, eds., Kluwer Academic, Dordrecht, Netherlands, pp. 359–368.

Shieh, W., Sun, F., and Chen, D., 2009, “On the Topological Representation and Compatibility of Variable Topology Mechanisms,” ASME Paper No. DETC2009-87205. [CrossRef]

Yan, H.-S., and Kuo, C.-H., 2006. “Topological Representations and Characteristics of Variable Kinematic Joints,” ASME J. Mech. Des., 128(2), pp. 384–391. [CrossRef]

Slaboch, B. J., and Voglewede, P. A., 2013. “Planar, Higher Variable Joints for Reconfigurable Mechanisms,” ASME Paper No. DETC2013-13120. [CrossRef]

Reuleaux, F., 1963, The Kinematics of Machinery, Dover Publications, Mineola, NY.

Sacks, E., and Joskowicz, L., 2010, The Configuration Space Method for Kinematic Design of Mechanism, The MIT Press, London.

Rimon, E., and Burdick, J., 1995, “A Configuration Space Analysis of Bodies in Contact—I. 1st Order Mobility,” Mech. Mach. Theory, 30(6), pp. 897–912. [CrossRef]

Rimon, E., and Burdick, J., 1995, “A Configuration Space Analysis of Bodies in Contact—II. 2nd Order Mobility,” Mech. Mach. Theory, 30(6), pp. 913–928. [CrossRef]

Latombe, J., 2001, Robot Motion Planning, 6th ed., Kluwer Academic Publishers, Norwell, MA.

Figures

Fig. 4

Different cases for revolute higher variable joints

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Fig. 3

Higher variable joints

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Fig. 2

(a) General profile of a joint. (b) The profiles of link 1 and link 2 constrain the motion of link 1 relative to link 2.

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Fig. 1

Rotational to translational variable joint

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Fig. 5

R₁P₁ variable joint

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Fig. 6

R₁R₂R₃ variable joint

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Fig. 7

Configuration space for a R_uP_v variable joint

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Fig. 8

General joint profile

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Fig. 11

Design configuration space representation of adjustable pliers

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Fig. 12

The R₁P₂ variable joint for adjustable pliers

The R1P2 variable joint for adjustable pliers

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Fig. 13

Different configurations of the R₁P₂ variable joint

Different configurations of the R1P2 variable joint

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Fig. 14

Design configuration space representation of adjustable pliers

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Fig. 9

A change of δ₁ in the radial direction

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Fig. 19

Knipex R₂ adjustable plier design

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Fig. 20

Craftsman R₁ adjustable plier design

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Fig. 10

The R_uP_v variable joints

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Fig. 16

R₃P₂ variable joint

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Fig. 17

R₃P₂ adjustable plier design

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Fig. 18

Adjustable plier designs

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Fig. 15

R₁P₂ adjustable plier design

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Slaboch BJ, Voglewede PA. Profile Synthesis of Planar Rotational–Translational Variable Joints. ASME. J. Mechanisms Robotics. 2014;6(4):041012-041012-9. doi:10.1115/1.4027700.

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Profile Synthesis of Planar Rotational–Translational Variable Joints

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