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.

References

References
1.
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
.
2.
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
.
3.
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
.
4.
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
.
5.
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.
6.
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
.
7.
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
8.
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
.
9.
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
.
10.
Seriani
,
S.
, and
Gallina
,
P.
,
2016
, “
Variable Radius Drum Mechanisms
,”
ASME J. Mech. Rob.
,
8
(
2
), p.
021016
.
11.
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
.
12.
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
.
13.
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
.
14.
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.
15.
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
.
16.
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
.
17.
Abbena
,
E.
,
Salamon
,
S.
, and
Gray
,
A.
,
2017
,
Modern Differential Geometry of Curves and Surfaces With Mathematica
,
CRC Press
, Boca Raton, FL.
18.
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.
19.
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
.
20.
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
.
21.
Carricato
,
M.
,
2013
, “
Direct Geometrico-Static Problem of Underconstrained Cable-Driven Parallel Robots With Three Cables
,”
ASME J. Mech. Rob.
,
5
(
3
), p.
031008
.
22.
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
.
You do not currently have access to this content.