Research Papers: Design of Mechanisms and Robotic Systems

A Review on Compliant Joints and Rigid-Body Constant Velocity Universal Joints Toward the Design of Compliant Homokinetic Couplings

[+] Author and Article Information
D. Farhadi Machekposhti

Department of Precision and Microsystems
Delft University of Technology,
Mekelweg 2,
Delft 2628 CD, The Netherlands
e-mail: d.farhadimachekposhti@tudelft.nl

N. Tolou

Department of Precision and Microsystems
Delft University of Technology,
Mekelweg 2,
Delft 2628 CD, The Netherlands
e-mail: n.tolou@tudelft.nl

J. L. Herder

Department of Precision and Microsystems
Delft University of Technology,
Mekelweg 2,
Delft 2628 CD, The Netherlands
e-mail: j.l.herder@tudelft.nl

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 28, 2013; final manuscript received December 3, 2014; published online January 15, 2015. Assoc. Editor: Chintien Huang.

J. Mech. Des 137(3), 032301 (Mar 01, 2015) (12 pages) Paper No: MD-13-1596; doi: 10.1115/1.4029318 History: Received December 28, 2013; Revised December 03, 2014; Online January 15, 2015

This paper presents for the first time a literature survey toward the design of compliant homokinetic couplings. The rigid-linkage-based constant velocity universal joints (CV joints) available from literature were studied, classified, their graph representations were presented, and their mechanical efficiencies compared. Similarly, literature is reviewed for different kinds of compliant joints suitable to replace instead of rigid-body joints in rigid-body CV joints. The compliant joints are compared based on analytical data. To provide a common basis for comparison, consistent flexure scales and material selection are used. It was found that existing compliant universal joints are nonconstant in velocity and designed based on rigid-body Hooke's universal joint. It was also discovered that no compliant equivalent exists for cylindrical, planar, spherical fork, and spherical parallelogram quadrilateral joints. We have demonstrated these compliant joints can be designed by combining existing compliant joints. The universal joints found in this survey are rigid-body non-CV joints, rigid-body CV joints, or compliant non-CV joints. A compliant homokinetic coupling is expected to combine the advantages of compliant mechanisms and constant velocity couplings for many applications where maintenance or cleanliness is important, for instance in medical devices and precision instruments.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Moon, Y. M., and Kota, S., 2002, “Design of Compliant Parallel Kinematic Machines,” ASME Paper No. DETC2002/MECH-34204. [CrossRef]
Perry, J. C., Oblak, J., Jung, J. H., Cikajlo, I., Veneman, J. F., Goljar, N., Bizovicar, N., Matjacic, Z., and Keller, T., 2011, “Variable Structure Pantograph Mechanism With Spring Suspension System for Comprehensive Upper-Limb Haptic Movement Training,” J. Rehab. Res. Dev., 48(4), pp. 317–334. [CrossRef]
Ishii, C., and Kamei, Y., 2008, “On Servo Experiment of a New Multi-DOF Robotic Forceps Manipulator for Minimally Invasive Surgery,” Proceeding of the 5th International Symposium on Mechanics and Its Applications, Amman, Jordan, May 27–29, pp. 1–6.
Chiang, C. H., 1988, Kinematics of Spherical Mechanisms, Cambridge University Press, Cambridge, UK.
Hunt, K. H., 1973, “Constant-Velocity Shaft Couplings: A General Theory,” J. Eng. Ind., 95(B), pp. 455–464. [CrossRef]
Rzeppa, A. H., 1928, “Constant Velocity Universal Joint,” U.S. Patent No. 1,665,280.
Culver, I. H., 1969, “Constant Velocity Universal Joint,” U.S. Patent No. 3,477,249.
Thompson, G. A., 2006, “Constant Velocity Coupling and Control System Therefore,” U.S. Patent No. 7,144,326.
Kocabas, H., 2007, “Design and Analysis of a Spherical Constant Velocity Coupling Mechanism,” ASME J. Mech. Des., 129(9), pp. 991–998. [CrossRef]
Howell, L. L., 2001, Compliant Mechanisms, Wiley, New York, p. 459.
Herder, J. L., and Van Den Berg, F. P. A., 2000, “Statically Balanced Compliant Mechanisms (SBCM's), and Example and Prospects,” Proceedings ASME DETC 26th Biennial, Mechanisms and Robotics Conference, Baltimore, MD, ASME Paper No. DETC2000/MECH-14144, pp. 553–560.
Berglund, M. D., Magleby, S. P., and Howell, L. L., 2000, “Design Rules for Selecting and Designing Compliant Mechanisms for Rigid-Body Replacement Synthesis,” Proceedings of the 26th Design Automation Conference, ASME DETC, Baltimore, MD, 14225.
Howell, L. L., and Midha, A., 1994, “A Method for the Design of Compliant Mechanisms With Small-Length Flexural Pivots,” ASME J. Mech. Des., 116(1), pp. 280–290. [CrossRef]
Hopkins, J. B., 2007, “Design of Parallel Flexure Systems via Freedom and Constraint Topologies (FACT),” Master thesis, Massachusetts Institute of Technology, Cambridge, MA.
Hopkins, J. B., and Culpepper, M. L., 2010, “Synthesis of Multi-Degree of Freedom Flexure System Concepts via Freedom and Constraint Topologies (FACT)—Part I: Principles,” J. Precis. Eng., 34(2), pp. 259–270. [CrossRef]
Martin, G. H., 1982, Kinematics and Dynamics of Machines, McGraw-Hill Book Company, New York.
Molly, H., and Bengisu, O., 1969, “Das Gleichgang–Gelenk im Symmetriespiegel (The Constant Velocity Joint in the Mirror of Symmetry),” Automob. Ind., 14(2), pp. 45–54.
McCarthy, J. M., and Soh, G. S., 2010, Geometric Design of Linkages, 2nd ed., Springer, New York. [CrossRef]
Xu, P., Jingjun, Y., Guanghua, Z., and Shusheng, B., 2007, “The Modeling of Leaf-Type Isosceles-Trapezoidal Flexural Pivots,” ASME Paper No. DETC2007-34981. [CrossRef]
Jingjun, Y., Xu, P., Minglei, S., Shanshan, Z., Shushing, B., and Guanghua, Z., 2009, “A New Large–Stroke Compliant Joint & Micro/Nano Positioner Design Based on Compliant Building Blocks,” ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots, London, UK, June 22–24, pp. 409–416.
Trease, B. P., Moon, Y. M., and Kota, S., 2005, “Design of Large-Displacement Compliant Joints,” ASME J. Mech. Des., 127(4), pp. 788–798. [CrossRef]
Hunt, K. H., 1983, “Structural Kinematics of In-Parallel-Actuated Robot-Arms,” ASME J. Mech. Des., 105(4), pp. 705–712. [CrossRef]
Rineer, A. E., 1979, “Constant Velocity Universal Joint,” U.S. Patent No. 4,133,189.
Sclater, N., and Chironis, N. P., 2001, Mechanisms and Mechanical Devices Sourcebook, 3rd ed., McGraw-Hill Book Company, New York.
Geisthoff, H., Welschof, H., and Herchenbach, P., 1966, “Quasi Homokinetic Double Hooke,” German Patent No. 1,302,735.
Geisthoff, H., Welschof, H., and Herchenbach, P., 1978, “Strictly Homokinetic Double Hooke,” German Patent No. 2,802,572.
Wier, F. L., 1968, “Constant Velocity Universal Joint,” U.S. Patent No. 3,385,081.
Fenaille, P., 1927, “Tracta Joint,” German Patent No. 617,356.
Fischer, I. S., 1999, “Numerical Analysis of Displacements in a Tracta Coupling,” J. Eng. Comput., 15(4), pp. 334–344. [CrossRef]
Freudenstein, F., and Maki, E. R., 1979, “Creation of Mechanisms According to Kinematic Structure and Function,” Environ. Plann. B, 6(4), pp. 375–391. [CrossRef]
Dodge, A. Y., 1941, “Constant Velocity Universal Joint,” U.S. Patent No. 2,255,762.
Baker, M. P., 1966, “Constant Velocity Universal Joint,” U.S. Patent No. 3,263,447.
Eccher, O. B., 1970, “Constant Velocity Universal Joint,” U.S. Patent No. 3,517,528.
Falk, J. B., 1975, “High Deflection Constant Speed Universal Joint,” U.S. Patent No. 3,924,420.
Yaghoubi, M., Mohtasebi, S. S., Jafary, A., and Khaleghi, H., 2011, “Design, Manufacture and Evaluation of a New and Simple Mechanism for Transmission of Power Between Intersecting Shafts up to 135 Degrees (Persian Joint),” J. Mech. Mach. Theory, 46(7), pp.861–868. [CrossRef]
Lobontiu, N., 2002, Compliant Mechanisms Design of Flexure Hinges, CRC Press, New York, pp. 72–82. [CrossRef]
Paros, J. M., and Weisbord, L., 1965, “How to Design Flexure Hinges,” Mach. Des., 37, pp. 151–156.
Smith, S. T., 2000, Flexures: Elements of Elastic Mechanisms, Gordon and Breach Science, New York.
Dirksen, F., and Lammering, R., 2011, “On Mechanical Properties of Planar Flexure Hinges of Compliant Mechanisms,” J. Mech. Sci., 2, pp. 109–117. [CrossRef]
Chen, G. M., Jia, J. Y., and Li, Z. W., 2005, “Right-Circular Corner-Filleted Flexure Hinges,” IEEE International Conference on Automation Science and Engineering, Edmonton, Canada, Aug. 1–2, pp. 249–253. [CrossRef]
Lobontiu, N., Paine, J. S. N., Malley, E. O., and Samuelson, M., 2002, “Parabolic and Hyperbolic Flexure Hinges: Flexibility, Motion Precision and Stress Characterization Based on Compliance Closed-Form Equations,” J. Precis. Eng., 26(2), pp. 183–192. [CrossRef]
Lobontiu, N., Paine, J. S. N., Garcia, E., and Goldfarb, M., 2002, “Design of Symmetric Conic-Section Flexure Hinges Based on Closed-Form Compliance Equations,” J. Mech. Mach. Theory, 37(5), pp. 477–498. [CrossRef]
Smith, S. T., Badami, V. G., Dale, J. S., and Xu, Y., 1997, “Elliptical Flexure Hinges,” Rev. Sci. Instrum., 68(3), pp. 1474–1483. [CrossRef]
Tian, Y., Shirinzadeh, B., Zhang, D., and Zhong, Y., 2010, “Three Flexure Hinges for Compliant Mechanism Designs Based on Dimensionless Graph Analysis,” J. Precis. Eng., 34(1), pp. 92–100. [CrossRef]
Haringx, J. A., 1949, “The Cross Spring Pivot as a Constructional Element,” Appl. Sci. Res., 1(1), pp. 313–332. [CrossRef]
Jensen, B. D., and Howell, L. L., 2002, “The Modeling of Cross-Axis Flexural Pivots,” J. Mech. Mach. Theory, 37(5), pp. 461–476. [CrossRef]
Martin, J., and Robert, M., 2011, “Novel Flexible Pivot With Large Angular Range and Small Center Shift to be Integrated Into a Bio-Inspired Robotic Hand,” J. Intell. Mater. Syst. Struct., 22(13), pp. 1431–1437. [CrossRef]
Xu, P., Jingjun, Y., Guanghua, Z., Shusheng, B., and Zhiwei, Y., 2008, “Analysis of Rotational Precision for an Isosceles-Trapezoidal Flexural Pivot,” ASME J. Mech. Des., 130(5), p. 052302. [CrossRef]
Xu, P., Jingjun, Y., Guanghua, Z., and Shusheng, B., 2008, “The Stiffness Model of Leaf-Type Isosceles Trapezoidal Flexural Pivots,” ASME J. Mech. Des., 130(8), p. 082303. [CrossRef]
Xu, P., Jingjun, Y., Guanghua, Z., and Shusheng, B., 2009, “A Novel Family of Leaf-Type Compliant Joints: Combination of Two Isosceles-Trapezoidal Flexural Pivots,” ASME J. Mech. Rob., 1(2), p. 021005. [CrossRef]
Xu, P., and Jingjun, Y., 2011, “ADLIF: A New Large-Displacement Beam-Based Flexure Joint,” J. Mech. Sci., 2, pp. 183–188. [CrossRef]
Henein, S., Droz, S., Myklebust, L., and Onillon, E., 2003, “Flexure Pivot for Aerospace Mechanisms,” Proceedings of the 10th European Space Mechanisms and Tribology Symposium, Sept. 24–26, San Sebastian, Spain, pp. 1–4.
Wiersma, D. H., Boer, S. E., Aarts, R. G. K. M., and Brouwer, D. M., 2012, “Large Stroke Performance Optimization of Spatial Flexure Hinges,” ASME Paper No. DETC2012-70502. [CrossRef]
Fowler, R. M., 2012, “Investigation of Compliant Space Mechanisms With Application to the Design of a Large-Displacement Monolithic Compliant Rotational Hinge,” Master thesis, Brigham Young University, Provo, UT.
Goldfarb, M., and Speich, J. E., 1999, “A Well-Behaved Revolute Flexure Joint for Compliant Mechanism Design,” ASME J. Mech. Des., 121(3), pp. 424–429. [CrossRef]
Goldfarb, M., and Speich, J. E., 2003, “Split Tube Flexure,” U.S. Patent No. 6,585,445.
Qizhi, Y., Xiaobing, Z., Long, C., and Pengfei, Z., 2011, “Analysis of Traditional Revolute Pair and the Design of a New Compliant Joint,” International Conference on Electric Information and Control Engineering (ICEICE), Wuhan, China, Apr. 15–17, pp. 2007–2009.
Berselli, G., Piccinini, M., and Vassura, G., 2011, “Comparative Evaluation of the Selective Compliance in Elastic Joints for Robotic Structures,” IEEE International Conference on Robotics and Automation, Shanghai, China, May 9–13, pp. 4626–4631. [CrossRef]
Balucani, M., Belfiore, N. P., Crescenzi, R., and Verotti, M., 2010, “The Development of a MEMS/NEMS-based 3 D.O.F. Compliant Micro Robot,” Proceedings of the 19th International Workshop on Robotics in Alpe-Adria-Danube Region, Budapest, Hungary, June 24–26 pp. 173–179. [CrossRef]
Hillberry, B. M., and Hall, A. S., 1976, “Rolling Contact Prosthetic Knee Joint,” U.S. Patent No. 3,945,053.
Mankame, N. D., and Ananthasuresh, G. K., 2002, “Contact Aided Compliant Mechanisms: Concept and Preliminaries,” ASME Paper No. DETC2002/MECH-34211. [CrossRef]
Jeanneau, A., Herder, J. L., Laliberte, T., and Gosselin, C., 2004, “A Compliant Rolling Contact Joint and Its Application in a 3-DOF Planar Parallel Mechanism With Kinematic Analysis,” ASME Paper No. DETC2004-57264. [CrossRef]
Cannon, J. R., and Howell, L. L., 2005, “A Compliant Contact-Aided Revolute Joint,” J. Mech. Mach. Theory, 40(11), pp. 1273–1293. [CrossRef]
Cannon, J. R., Lusk, C. P., and Howell, L. L., 2005, “Compliant Rolling-Contact Element Mechanisms,” ASME Paper No. DETC2005-84073. [CrossRef]
See supplementary material Appendices A, B, C, and D for the related formulas for the given results in Table 2, Table 4, Table 5, and Table 6, respectively.
Lobontiu, N., and Garcia, E., 2003, “Two-Axis Flexure Hinges With Axially-Collocated and Symmetric Notches,” Comput. Struct., 81(13), pp. 1329–1341. [CrossRef]
Stark, J. A., 1958, “Flexible Couplings,” U.S. Patent No. 2,860,495.
Tanik, E., and Parlaktas, V., 2012, “Compliant Cardan Universal Joint,” ASME J. Mech. Des., 134(2), p. 021011. [CrossRef]
Lobontiu, N., and Paine, J. S. N., 2002, “Design of Circular Cross-Section Corner-Filleted Flexure Hinges for Three-Dimensional Compliant Mechanisms,” ASME J. Mech. Des., 124(3), pp. 479–484. [CrossRef]
Cannon, B. R., Lillian, T. D., Magleby, S. P., Howell, L. L., and Linford, M. R., 2005, “A Compliant End-Effector for Microscribing,” Precis. Eng., 29(1), pp. 86–94. [CrossRef]
Lin, Y. T., and Lee, J. J., 2007, “Structural Synthesis of Compliant Translational Mechanisms,” 12th IFToMM World Congress, Besancon, France, June 18–21, pp. 1–5.
Mackay, A., 2007, “Large Displacement Linear Motion Compliant Mechanisms,” Master's thesis, Brigham Young University, Provo, UT.
Jones, R. V., 1951, “Parallel and Rectilinear Spring Movements,” J. Sci. Instrum., 28(2), pp. 38–41. [CrossRef]
Kyusojin, A., and Sagawa, D., 1988, “Development of Linear and Rotary Movement Mechanism by Using Flexible Strips,” Bull. Jpn. Soc. Precis. Eng., 22(4), pp. 309–314.
Hubbard, N. B., Wittwer, J. W., Kennedy, J. A., Wilcox, D. L., and Howell, L. L., 2004, “A Novel Fully Compliant Planar Linear-Motion Mechanism,” ASME Paper No. DETC2004-57008. [CrossRef]


Grahic Jump Location
Fig. 1

Schematic representation of the classification levels to compare the rigid-body CV joints

Grahic Jump Location
Fig. 2

Graph representation for linkage type rigid-body CV joints

Grahic Jump Location
Fig. 3

Compliant revolute joints; (a) rectangular, (b) RCCF, (c) circular, (d) “a” parabolic, “b” hyperbolic, “c” elliptical, “d” cycloidal, (e) V-shape, (f) cross axis, (g) cartwheel, (h) X2, (i) LITF, (j) ADLIF, (k) butterfly, (l) CR-1, (m) CR-2, (n) ∞-flexure hinge, (o) CR-3, (p) multileaf, (q) multileaf spring, (r) split-tube-1(ST-1), (s) ST-2, (t) spiral, (u) helical, (v) annulus-shape, (w) revolute pair, (x) XR-joint, (y) contact-aided, and (z) rolling contact-2

Grahic Jump Location
Fig. 6

Compliant translational joints: (a) four-bar-notch block and (b) double notch block, (c) symmetrical double notch block, (d) four-bar block, (e) double block, (f) symmetrical double block, (g) folded beam, (h) planar CT joint, and (i) double XBob

Grahic Jump Location
Fig. 7

The range of motion, the dimensionless ratios of off-axis rotational stiffness to on-axis rotational stiffness, axis drift, and size of each compliant revolute joint, if data were available. The values were normalized to the largest in the group, shown in logarithmic scale. The flexure types are notch-type (N-T), leaf-spring (L-S), and tap-spring (T-S).

Grahic Jump Location
Fig. 8

The dimensionless ratio for range of motion (δ*), the dimensionless ratio of off-axis translational stiffness to on-axis translational stiffness (γ), and size of each compliant translational joint, if data were available. The values were normalized to the largest in the group, shown in logarithmic scale. The flexure types are notch-type (N-T) and leaf-spring (L-S).

Grahic Jump Location
Fig. 9

Proposed: (a) compliant spherical fork joint, (b) compliant cylindrical joint, and (c) compliant planar joint as an example

Grahic Jump Location
Fig. 10

Proposed compliant homokinetic coupling based on Double-Hooke's universal joint as an example

Grahic Jump Location
Fig. 4

Compliant universal joints; (a) two-axis flexure joint, (b) notch U joint-1, (c) notch U joint-2, (d) collinear notch joint, (e) CU joint, (f) XU-joint, (g) Stark-1, (h) Stark-2, and (i) compliant cardan U joint

Grahic Jump Location
Fig. 5

Compliant spherical joints: (a) three-axis flexure joint and (b) CS joint




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In