Nabil Simaan
Parallel manipulation is relatively a new field in robotics. The development in this
field intensified during the last two decades; however, there are still unsolved problems to be
investigated in this field. These problems include kinematic modeling and synthesis of new
parallel architectures and singularity analysis. The solution of the forward kinematics of a
general 6 DOF fully parallel manipulator is only three years old and the first example of a
general 6 DOF fully parallel manipulator with 40 real solutions is only one year old. Although
during the last decade there were many attempts for implementation of parallel robots, the full
merits of these architectures were not fully understood and exploited. Serial manipulators feature a large work volume and high dexterity, but suffer from
several inherent disadvantages. These disadvantages include low precision, poor force
exertion capability and low payload-to-weight ratio, motors that are not located at the base,
large number of moving parts leading to high inertia.
The low precision of these robots stems from cumulative joint errors and deflections in
the links. The low payload-to-weight ratio stems form the fact that every actuator supports the
weight of the successor links. The high inertia is due to the large number of moving parts that
are connected in series, thus, forming long beams with high inertia.
The hybrid architecture
Fully parallel and non-fully parallel manipulators
Analysis and Synthesis of Parallel Robots for Medical Applications
RESEARCH THESIS
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE IN MECHANICAL ENGINEERING
SUBMITTED TO THE SENATE OF
THE TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY
HAIFA
July 99
You can download the entire thesis:
http://www.columbia.edu/cu/mece/arma/people/nabil_simaan/MSResearch_thesis.pdf
Robot assisted surgery is also a new trend of development in surgery. Assimilating a
robotic assistant in the surgical arena as an additional smart and precise tool bears numerous
advantages. These advantages include broadening the capabilities of the surgeon in
performing precise procedures and uplifting the burden of routine tasks. The intrinsic
characteristics of parallel robots are discussed in this work and shown to suit the requirements
of a robotic assistant better than the characteristics of serial robots.
Based on these facts, we aim our work towards developing a mini parallel robot for
medical applications and exploring new parallel architectures. The work presents a taskoriented
synthesis and design of a mini parallel robot for medical applications. Two robotic
architectures (the RSPR and the USR robots), which are modifications of known structures,
are presented in detail and compared in terms of required actuator forces, minimal
dimensions, workspace, and practical design considerations. The work includes type and
dimensional synthesis for the suggested architectures, Jacobian formulation, and singularity
analysis for a class of non-fully parallels robots.
The Jacobian formulation presented in this work provides a method for classifying the
non-fully parallel robots and grouping several architectures in families with common Jacobian
formulation and singularity analysis. In particular, the formulation presented here groups 14
non-fully parallel robots into one family. This formulation also shows that all these 14
manipulators share the same parallel singularities due to a tripod mechanism common to all
these manipulators. The singularity analysis and Jacobian formulation are based on
geometrical understanding of the system, thus, providing easy method for physical
interpretation of singularities and deducing conclusions regarding possible elimination of
singularities by altering the geometrical characteristics of the robots.
The comparison between the USR and the RSPR robots shows that the RSPR robot
better suits the procedure in hand than the USR robot in terms of smaller required actuator
forces. The singularity analysis highlights an additional advantage of the RSPR over the USR
robot in terms of having less singular configurations.
Based on the results of the comparison and the dimensional synthesis we constructed a
prototype of a medical robotic assistant. We also implemented position control and wrote the
control program that allows activating the prototype in a Master-Slave mode. This prototype
features a new parallel architecture based on the RSPR concept, low weight, compactness,
and accuracy. These characteristics promise successful future implementation of this
prototype for laparoscope manipulation and knee surgery.
Three robotic architectures
The three basic robot architectures are:
a) Serial architecture
b) Parallel architecture
c) Hybrid architecture.
The serial architecture
This is the classical anthropomorphic architecture for robot manipulators, Fig. 1.1. In
this architecture, the output link is connected to the base link by a single open loop kinematic
chain. The kinematic chain is composed from a group of rigid links where each pair of
adjacent links are interconnected by an active kinematic pair (controlled joint).
Another disadvantage of serial manipulators is the existence of multiple solutions to
the inverse kinematics problem. The inverse kinematics problem is defined as finding the
required values of the active joints that correspond to a desired position and orientation of the
output link. The solution of the inverse kinematic problem is a basic control algorithm in
robotics; therefore, the existence of multiple solutions to the inverse kinematics problem
complicates the control algorithm. The direct kinematics problem of serial manipulators has
simple and single-valued solution. However, this solution is not required for control purposes.
The direct kinematics problem is defined as calculating the position and orientation of the
output link for a given set of active joints’ values.
The low precision and payload-to-weigh ratio lead to expensive serial robots utilizing
extremely accurate gears and powerful motors. The high inertia disadvantage prevents the use
of serial robots for applications requiring high accelerations and agility, such as flight
simulation and very fast pick and place tasks.
The parallel architecture
This non-anthropomorphic architecture for robot manipulators, although known for a
century, was developed mainly during the last two decades. This architecture is composed of
an output link connected to a base link by several kinematic chains, Fig 1.2. Motion of the
output link is achieved by simultaneous actuation of the kinematic chains’ extremities.
Similarly, the load carried by the output link is supported by the various kinematic chains;
therefore, this architecture is referred to as parallel architecture. In contrast with the openchain
serial manipulator, the parallel architecture is composed of closed kinematic chains only
and every kinematic chain includes both active and passive kinematic pairs.
Parallel manipulators exhibit several advantages and disadvantages. The disadvantages
of the parallel manipulators are limited work volume, low dexterity, complicated direct
kinematics solution, and singularities that occur both inside and on the envelope of the work
volume. However, the parallel architecture provides high rigidity and high payload-to-weight
ratio, high accuracy, low inertia of moving parts, high agility, and simple solution for the
inverse kinematics problem. The fact that the load is shared by several kinematic chains
results in high payload-to-weight ratio and rigidity. The high accuracy stems from sharing, not
accumulating, joint errors.
Based on the advantages and disadvantages of parallel robots it can be concluded that
the best suitable implementations for such robots include requirements for limited workspace,
high accuracy, high agility, and a lightweight and a compact robot. These ideal
implementations exploit both the disadvantages and advantages of the parallel architecture.
The combination of both open and closed kinematic chains in a mechanism leads to a
third architecture, which is referred to as the hybrid architecture. This architecture combines
both advantages and disadvantages of the serial and parallel mechanisms. Fig. 1.3 presents an
example of a hybrid manipulator constructed from two parallel manipulators connected in
series.
There are two major categories of parallel robots. These categories are the fully
parallel robots, and the non-fully parallel robots. The distinction between these categories is
based on the following definition. This definition is the same as the one presented in [Chablat
and Wenger, 1998].
A fully parallel manipulator is a parallel mechanism satisfying the following
conditions:
1) The number of elementary kinematic chains equals the relative mobility
(connectivity) between the base and the moving platform.
2) Every kinematic chain possesses only one active joint.
3) All the links in the kinematic chains are binary links, i.e. no segment of an
elementary kinematic chain can be linked to more than two bodies.
Based on the solution multiplicity of the inverse kinematics problem this limiting
definition can be summarized as follows. A fully parallel manipulator has one and only one
solution to the inverse kinematics problem. Any parallel manipulator with multiple solutions
for the inverse kinematics problem is a non-fully parallel manipulator.