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Research Papers: Design of Mechanisms and Robotic Systems

# A Fully Compliant Homokinetic Coupling

[+] Author and Article Information

Mechatronic System Design Group,
Department of Precision and
Microsystems Engineering,
Delft University of Technology,
Delft 2628 CD, The Netherlands

N. Tolou, J. L. Herder

Mechatronic System Design Group,
Department of Precision and
Microsystems Engineering,
Delft University of Technology,
Delft 2628 CD, The Netherlands

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 12, 2017; final manuscript received August 5, 2017; published online November 9, 2017. Assoc. Editor: Massimo Callegari.

J. Mech. Des 140(1), 012301 (Nov 09, 2017) (9 pages) Paper No: MD-17-1126; doi: 10.1115/1.4037629 History: Received February 12, 2017; Revised August 05, 2017

## Abstract

This paper introduces a homokinetic coupling, a constant velocity universal joint (CV joint), which is fully compliant and potentially monolithic. The proposed compliant design can accommodate high misalignment angles between the input and the output rotational axes. Additional kinematic constraints are applied to well-known Double Hooke's universal joint, to guarantee a one-to-one constant velocity rotation transmission for all different misalignment angles. The influence of the extra constraints on degrees-of-freedom (DOF) of the mechanism is studied using screw theory. Furthermore, it was shown that the mechanism is yet a 1DOF linkage for rotation transmission and a 2DOF rotational joint as all universal joints. The kinematics of the mechanism is studied, and constant velocity conditions are identified. The pseudo-rigid-body model (PRBM) of the new angled arrangement of the Double Hooke's universal joint is created, and the input–output torque relationship is then studied. The different possible compliant embodiments based on the PRBM model were discussed and illustrated. Moreover, one of the proposed compliant counterparts is dimensioned as a power transmission coupling for a high misalignment angle, up to $45 deg$. Further, a prototype was manufactured for the experimental evaluation, and it is shown that the results are consistent with the PRBM and the finite element model.

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## References

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## Figures

Fig. 1

6R spatial overconstrained linkages: (a) Bennett 6R hybrid linkage, (b) Double Hooke's universal joint arrangement, and (c) an angled arrangement of Double Hooke's universal joint

Fig. 2

Angled arrangement of the Double Hooke's universal joint; linkage arrangement, coordinate systems, and parameters

Fig. 3

Graph representations for the DOF analysis: (a) as a rotation transmission system with only one set of 6R linkage and (b) as a two rotational DOF kinematic pair with at least n number of similar sets of 4R linkage, which are placed with an angular offset between the input and the output axes. The circles in the graphs indicate different links and the lines represent different revolute joints of the mechanism shown in Fig. 2. “G” indicates the fixed link and “EE” indicates the end effector which is the output shaft.

Fig. 4

Pseudo-rigid-body model of the angled arrangement of the Double Hooke's universal joint

Fig. 5

Proposed compliant configurations for the PRBM model of the angled arrangement of the Double Hooke's universal joint by means of rigid-body replacement synthesis. Replacing the conventional revolute joint by (a) a small length flexure and (b) a compliant cross flexure.

Fig. 6

Axis deviation of flexures from their original position, axis drift, cannot change the homokinetic conditions

Fig. 8

The prototype of the fully compliant homokinetic coupling, compliant CV joint, the rigid parts are fabricated out of Aluminum, and the flexures are cut out of austenitic stainless steel

Fig. 7

Fully compliant homokinetic couplings based on the angled arrangement of the Double Hooke's universal joint, (a) there is one decoupled coupler link corresponding to each compliant set and (b) all the compliant sets sharing one coupler link and move simultaneously

Fig. 10

The measurement setups (a) to analyze the input–output angular velocity relationship and (b) to study the input–output rotational stiffness, Kr , of the design. In both figures, the setup is adjusted for the misalignment angle of ψ=45 deg.

Fig. 11

The kinematic model and experimental data for the input–output angular velocity relationship of the compliant homokinetic coupling. The experimental data were recorded at three different misalignment angles: ψ=15 deg,  30 deg, and 45 deg.

Fig. 12

Results of the moment-angular displacement characteristic, the input–output rotational stiffness Kr , of the compliant homokinetic coupling at ψ=45 deg misalignment angle. Experimental data (Exp) were evaluated for the design with three compliant sets, n = 3. Besides, finite element modeling is shown for three, four, and five compliant sets, n = 3, 4, and 5.

Fig. 9

Predicted stress of the compliant homokinetic coupling under 45 deg misalignment angle between the input and the output axes

Fig. 13

Measurement setup to evaluate the actuation stiffness

Fig. 14

Actuation torque required to deal with the internal stiffness of the compliant homokinetic coupling. Results are from finite element modeling, PRBM model, and experimental evaluation (Exp) for different number of compliant sets, n = 3, 4, and 5. The results for all cases were performed at ψ=45 deg misalignment angle.

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