Differential Noncircular Pulleys for Cable Robots and Static Balancing

Dmitri Fedorov,Lionel Birglen

doi:10.1115/1.4041213

Abstract

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.

Highlights

IntroductionUnlike with their circular counterparts, the length of cable which is wound or released during the rotation of a noncircular pulley ( referred to as a noncircular spool or a variable-radius drum) is a nonlinear function of its rotation angle and is highly sensitive to its profile
Unlike with their circular counterparts, the length of cable which is wound or released during the rotation of a noncircular pulley is a nonlinear function of its rotation angle and is highly sensitive to its profile
We introduce a serial cable routing for antagonistic pulleys, similar to that of the classical Weston differential [14], in which the position of an idler pulley is guided by a cable simultaneously winding on one noncircular pulley while unwinding from another

Summary

Introduction

Unlike with their circular counterparts, the length of cable which is wound or released during the rotation of a noncircular pulley ( referred to as a noncircular spool or a variable-radius drum) is a nonlinear function of its rotation angle and is highly sensitive to its profile. 2.2 Graphical Synthesis As mentioned, the winding or unwinding of a noncircular pulley can be described as the function relating the relative angle θP to x, the distance from points O to P, and the cable length lFV. Notice in this figure how, while the tension generated by the spring increases when the pulley rotates, the moment arm of the spring force decreases to keep the generated torque around O constant. To keep the cable length constant, the distance x between the noncircular and idler pulleys must vary for the cable to be kept taut This can be realized by either relying on gravity (see the first application example, Section 4.1), or by a spring (see the second application example, Section 4.2).

Graphical Synthesis

Second Example

Discussion

Conclusion