Venkat Krovi
†
e-mail: vkrovi@eng.buffalo.edu
G. K. Ananthasuresh
e-mail: gksuresh@grip.cis.upenn.edu
Vijay Kumar
e-mail: kumar@grip.cis.upenn.edu
Mechanical Engineering and Applied Mechanics,
University of Pennsylvania,
Room 301C, GRASP Lab,
3401 Walnut Street,
Philadelphia, PA 19104
Kinematic and Kinetostatic
Synthesis of Planar Coupled
Serial Chain Mechanisms
Single Degree-of-freedom Coupled Serial Chain (SDCSC) mechanisms form a novel class
of modular and compact mechanisms with a single degree-of-freedom, suitable for a
number of manipulation tasks. Such SDCSC mechanisms take advantage of the hardware
constraints between the articulations of a serial-chain linkage, created using gear-trains
or belt/pulley drives, to guide the end-effector motions and forces. In this paper, we
examine the dimensional synthesis of such SDCSC mechanisms to perform desired planar
manipulation tasks, taking into account task specifications on both end-effector motions
and forces. Our solution approach combines precision point synthesis with optimization to
realize optimal mechanisms, which satisfy the design specifications exactly at the selected
precision points and approximate them in the least-squares sense elsewhere along a
specified trajectory. The designed mechanisms can guide a rigid body through several
positions while supporting arbitrarily specified external loads. Furthermore, torsional
springs are added at the joints to reduce the overall actuation requirements and to en-
hance the task performance. Examples from the kinematic and the kinetostatic synthesis of
planar SDCSC mechanisms are presented to highlight the benefits.
DOI: 10.1115/1.1464563
1 Introduction
Typical manipulation tasks require specification of the motion
of the manipulated object as well as its force interactions with the
environment. Further, many such tasks are inherently single
degree-of-freedom d.o.f., parameterizable by a single variable
such as the arc-length parameter. Hence, we introduce a novel
configuration called Single Degree-of-freedom Coupled Serial
Chain SDCSC mechanisms for executing such single degree-of-
freedom manipulation tasks.
A variety of closed-loop mechanisms and general-purpose se-
rial chain manipulators have been used in the past to accomplish
such manipulation tasks. Four-bar linkages, such as the one shown
in Fig. 1a, can generate a wide variety of the desired trajectories
using a single actuator but tend to be unsuitable for cluttered
environments due to the interference of the links with each other
and with the environment. Serial chain manipulator configura-
tions, such as the one shown in Fig. 1b, are therefore preferred
in cluttered environments but require multiple articulations and
hence actuators and coordinated control. Constraints need to be
created between the joint articulations, in software, to accomplish
the single degree-of-freedom manipulation tasks. While, the soft-
ware reconfigurability of the constraints offers considerable flex-
ibility, it comes at the price of increased complexity of actuation,
coordination and control, especially for specialized or repetitive
tasks. Tendon-driven serial-chain manipulators, such as the one
shown in Fig. 1c, permit the relocation of the actuators to the
base of the manipulator, thereby reducing the inertia of the mov-
ing parts, but still require at least as many actuators as degrees of
freedom.
SDCSC mechanisms are proposed here as an alternative to both
closed-loop and serial chain linkages. Such mechanisms may be
constructed by mechanically coupling the rotations of the links of
an n-link, n-d.o.f. serial chain manipulator using cable and pulley
drives or by gear-trains. Each coupling between two successive
joint rotations reduces one degree-of-freedom and repeated cou-
pling reduces the overall degrees of freedom of the manipulator to
one, as shown in Fig. 1d. The resulting SDCSC mechanisms
combine the simplicity of single-degree-of-freedom control and
rigidity/strength afforded by closed-loop linkages with the modu-
larity, compactness and reduced interference of serial chains.
SDCSC mechanisms can be used to realize a range of end-effector
trajectories using just one degree of freedom. Trajectories of in-
creasing complexity and variety may be generated by increasing
the number of links of the SDCSC mechanism, as illustrated in
Fig. 2. In this paper, our interest is in developing dimensional
synthesis tools to aid the design of SDCSC mechanisms for de-
sired manipulation tasks.
Our work is motivated by the design of customized rehabilita-
tion aids for the disabled 1. The design requirement is for cre-
ation of passive articulated manipulators, which can be actuated
by alternate functional body parts of the user e.g., legs for hand
amputees or head for quadriplegics to realize a set of motions and
forces. The passivity of mechanical constraint implementation, re-
duced interference with the environment, simplicity of control and
low cost favor the use of the SDCSC configuration for such tasks.
Figure 3a shows the fabricated prototype of a feeding mecha-
nism, which powered solely by the motions of the quadriplegic
user’s head, permits the user to feed independently. This feeder
features a SDCSC type manipulator in the sagittal plane and in
this paper, we will examine the shaping of the end-effector motion
and input torque profile in the examples.
Some of the above discussed benefits also make such SDCSC
configurations attractive for use in assembly tasks in manufactur-
ing plants, either as a low cost solution automation solution or to
work in cooperation with the human operator. Further, the design
may be enhanced easily by permitting all the principal structural
parameters for a given SDCSC manipulator, such as link lengths,
coupling ratios and initial posture, to be adjustable. Figure 3b
depicts an industrial application of such a reconfigurable manipu-
lation assist device, where the end-effector forms a passive virtual
guide rail to constrain and redirect the motions and forces of the
user to the prescribed task-space curve while retaining the ability
to be reconfigured to realize other constrained motions 2.
Finally, the kinetostatic design and optimization methods pre-
²
Currently with the Department of Mechanical and Aerospace Eng., SUNY Buf-
falo.
Contributed by the Mechanisms Committee for publication in the JOURNAL OF
MECHANICAL DESIGN. Manuscript received February 2000. Associate Editor: G. S.
Chirikjian.
Copyright © 2002 by ASME Journal of Mechanical Design JUNE 2002, Vol. 124 Õ 301