Research Papers

Differential Noncircular Pulleys for Cable Robots and Static Balancing

[+] Author and Article Information
Dmitri Fedorov

Department of Mechanical Engineering,
Polytechnique Montréal,
Montréal, QC H3T 1J4, Canada
e-mail: dmitri.fedorov@polymtl.ca

Lionel Birglen

Department of Mechanical Engineering,
Polytechnique Montréal,
Montréal, QC H3T 1J4, Canada
e-mail: lionel.birglen@polymtl.ca

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received February 26, 2018; final manuscript received August 8, 2018; published online September 7, 2018. Assoc. Editor: Marc Gouttefarde.

J. Mechanisms Robotics 10(6), 061001 (Sep 07, 2018) (8 pages) Paper No: JMR-18-1051; doi: 10.1115/1.4041213 History: Received February 26, 2018; Revised August 08, 2018

In this paper, we introduce a mechanism consisting of a pair of noncircular pulleys with a constant-length cable. While a single noncircular pulley is generally limited to continuously winding or unwinding, the differential cable routing proposed here allows to generate nonmonotonic motions at the output of the arrangement, i.e., the location of the idler pulley redirecting the cable. The equations relating its motion to rotation angles of the noncircular pulleys and to the cable length are presented in the first part of this paper. Next, we introduce a graphical method allowing us to obtain the required pulley profiles for a given output function. Our approach is finally demonstrated with two application examples: the guiding of a cable-suspended robot along a complex trajectory using a single actuator, and the static balancing of a pendulum with a 360 deg rotational range of motion.

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Shirafuji, S. , Ikemoto, S. , and Hosoda, K. , 2017, “Designing Noncircular Pulleys to Realize Target Motion Between Two Joints,” IEEE/ASME Trans. Mechatronics, 22(1), pp. 487–497. [CrossRef]
Stachel, H. , 2009, Gears and Belt Drives for Non-Uniform Transmission, In: Ceccarelli M. eds., Proceedings of EUCOMES 08, Springer, Dordrecht, The Netherlands, pp. 415–422.
Schmit, N. , and Okada, M. , 2013, “Optimal Design of Nonlinear Springs in Robot Mechanism: Simultaneous Design of Trajectory and Spring Force Profiles,” Adv. Rob., 27(1), pp. 33–46. [CrossRef]
Shin, D. , Yeh, X. , and Khatib, O. , 2013, “Circular Pulley Versus Variable Radius Pulley: Optimal Design Methodologies and Dynamic Characteristics Analysis,” IEEE Trans. Rob., 29(3), pp. 766–774. [CrossRef]
Fiorio, L. , Romano, F. , Parmiggiani, A. , Sandini, G. , and Nori, F. , 2014, “Stiction Compensation in Agonist-Antagonist Variable Stiffness Actuators,” Robotics: Science and Systems, Proceedings of Robotics: Science and Systems, Berkeley, CA, July.
Ulrich, N. , and Kumar, V. , 1991, “Passive Mechanical Gravity Compensation for Robot Manipulators,” IEEE International Conference on Robotics and Automation, Sacramento, CA, Apr. 9–11, pp. 1536–1541.
Herder, J. , 2001, “Energy-Free Systems: Theory, Conception, and Design of Statically Balanced Spring Mechanisms,” Ph.D. thesis, TU Delft, Delft University of Technology, Delft, The Netherlands. https://repository.tudelft.nl/islandora/object/uuid:8c4240fb-0315-462a-8b3b-efbd0f0e68b6
Endo, G. , Yamada, H. , Yajima, A. , Ogata, M. , and Hirose, S. , 2010, “A Passive Weight Compensation Mechanism With a Non-Circular Pulley and a Spring,” IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, May 3–7, pp. 3843–3848.
Cui, M. , Wang, S. , and Li, J. , 2015, “Spring Gravity Compensation Using the Noncircular Pulley and Cable for the Less-Spring Design,” 14th IFToMM World Congress, Tapei, Taiwan, Oct. 25–30, pp. 135–143.
Seriani, S. , and Gallina, P. , 2016, “Variable Radius Drum Mechanisms,” ASME J. Mech. Rob., 8(2), p. 021016. [CrossRef]
Scalera, L. , Gallina, P. , Seriani, S. , and Gasparetto, A. , 2018, “Cable-Based Robotic Crane (Cbrc): Design and Implementation of Overhead Traveling Cranes Based on Variable Radius Drums,” IEEE Trans. Rob., 34(2), pp. 474–485. [CrossRef]
Khakpour, H. , Birglen, L. , and Tahan, S.-A. , 2014, “Synthesis of Differentially Driven Planar Cable Parallel Manipulators,” IEEE Trans. Rob., 30(3), pp. 619–630. [CrossRef]
Khakpour, H. , and Birglen, L. , 2014, “Workspace Augmentation of Spatial 3-DOF Cable Parallel Robots Using Differential Actuation,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2014), Chicago, IL, Sept. 14–18, pp. 3880–3885.
Hong, D, W. , and Cipra, J. R. , 2003, “A Method for Representing the Configuration and Analyzing the Motion of Complex Cable-Pulley Systems,” ASME J. Mech. Des., 125(2), pp. 332–341.
Kim, B. , and Deshpande, A. D. , 2014, “Design of Nonlinear Rotational Stiffness Using a Noncircular Pulley-Spring Mechanism,” ASME J. Mech. Rob., 6(4), p. 041009. [CrossRef]
Schmit, N. , and Okada, M. , 2012, “Design and Realization of a Non-Circular Cable Spool to Synthesize a Nonlinear Rotational Spring,” Adv. Rob., 26(3–4), pp. 234–251. [CrossRef]
Abbena, E. , Salamon, S. , and Gray, A. , 2017, Modern Differential Geometry of Curves and Surfaces With Mathematica, CRC Press, Boca Raton, FL.
Thompson, R. R. , and Blackstone, M. S. , 2005, “Three-Dimensional Moving Camera Assembly With an Informational Cover Housing,” U.S. Patent No. 6,873,355.
Pusey, J. , Fattah, A. , Agrawal, S. , and Messina, E. , 2004, “Design and Workspace Analysis of a 6–6 Cable-Suspended Parallel Robot,” Mech. Mach. Theory, 39(7), pp. 761–778. [CrossRef]
Gouttefarde, M. , and Gosselin, C. M. , 2006, “Analysis of the Wrench-Closure Workspace of Planar Parallel Cable-Driven Mechanisms,” IEEE Trans. Rob., 22(3), pp. 434–445. [CrossRef]
Carricato, M. , 2013, “Direct Geometrico-Static Problem of Underconstrained Cable-Driven Parallel Robots With Three Cables,” ASME J. Mech. Rob., 5(3), p. 031008. [CrossRef]
Bijlsma, B. G. , Radaelli, G. , and Herder, J. L. , 2017, “Design of a Compact Gravity Equilibrator With an Unlimited Range of Motion,” ASME J. Mech. Rob., 9(6), p. 061003. [CrossRef]


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Fig. 1

Geometry of a single noncircular pulley

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Fig. 2

Illustration of the proposed noncircular pulley synthesis method. In (a), the target function g(θP, x, lFV) = 0 is shown, in (b), the involute curve is drawn, and, in (c) the pulley shape is obtained from the latter curve. The rotation of the noncircular pulley in the external axes system is shown in (d).

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Fig. 3

Proposed synthesis method with a nonzero idler pulley radius. In (a), the involute curve is drawn, and, in (b), the pulley shape is obtained from the latter curve. The rotation of the noncircular pulley in the external axes system is shown in (c).

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Fig. 4

Geometry of the serial cable routing for antagonistic noncircular pulleys

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Fig. 5

Proposed synthesis method for the differential case. In (a), the target distance is shown, in (b), the length of cable transferred from lF+V to lF−V is illustrated, in (c), the involute curves are drawn, and, in (d), the winding pulley shape is obtained from its involute curve. The rotation of the differential pulley system in the external axes system is shown in (e).

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Fig. 6

Trajectory guiding for a cable-suspended robot. In (a), the 3D model of the prototype is shown. In (b), the target distance function is illustrated. This function can be generated using the pair of differential noncircular pulleys shown in (c).

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Fig. 7

Experimental results for the trajectory guiding robot. In (a), an overall view of the prototype is provided, with a composite photograph of its motion shown in (b). Position measurements (scattered points), are superimposed on the expected trajectory (continuous trajectory) in (c). In (d), the trajectory is unfolded to show the experimental deviations.

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Fig. 8

Static balancing of a pendulum. In (a), the constant total energy is shown for −π < ϕ < pi. In (b), the target distance function is illustrated for both considered designs.

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Fig. 9

Two implementations of a static balancing mechanism. In (a), the motion of the idler pulley is a translation (design #1), while in (b), it is a rotation (design #2).

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Fig. 10

Static balancing prototype shown for various pendulum angles

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Fig. 11

Experimental results for the static balancing prototype. The minimal and maximal compensated torques are shown for various pendulum angles.



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