Multi Degree of Freedom (DOF) planar kinematic chains can be considered for application as parallel robots in view of their greater rigidity. A large number of distinct chains are available with the same number of links and DOF for consideration as parallel structures. Hence, it becomes necessary to know which of these chains more parallel so that the selection of these chains for the specified tasks like workspace and rigidity becomes easy. A simple and logical method is presented in this paper to accomplish the same. The measure of compactness developed in this paper enables comparison of distinct chains for these characteristics.

Robot arms which have received greater attention in the recent past are open chains, i.e., serial type linkages. Each joint in these robot arms is actuated independently. While possessing many advantages such as large workspace and maneuverability, they do suffer from disadvantages like less rigidity and accumulation of mechanical errors from shoulder to the end effector control problems. An alternative to the open chain robot arm is the parallel actuator arrangement.

It is widely accepted that a serial chain is less rigid when compared to a parallel chain, but will have greater workspace. Also, the accumulation of joint errors is more in serial chains. No attempt is made in this paper to compare the serial chains with parallel chains. Comparison is only among the distinct parallel structures with the same number of links and DOF. When we compare the chains for rigidity, we consider the same number, type and size of links which are assembled differently to form different structures. Comparison is also made for the specified task. Hence it is only necessary to compare all the distinct parallel chains with the same number of links and DOF for the extent of parallelism so that the above qualities can be assessed.

Generation of kinematic chains has been reported by many investigators. All the methods need tests for isomorphism in order to isolate distinct kinematic chains. Consequently, a number of methods for testing isomorphism have been developed and significant methods among these have been reviewed and listed in Tischler et al. (1975) and hence not repeated here with the belief that kinematic analysis and synthesis should not end up only with the generation of distinct kinematic chains. Holland II (1975) with his colleagues and students developed genetic algorithms which consider the process of competition, reproduction and the struggle for survival. Goldberg (1989) has made major contributions to this area and illustrated an introductory chapter on genetic algorithms with a group of four 5-bit binary strings. The works of Goldberg (1989) and Holland II (1975) come under the study of evolution of intelligence. In this context, the work of Roster (1997) which deals with the hazards in design methodologies of evolutionary algorithms in engineering is noteworthy. However, with the increasing applications of neural networks in engineering and technology more emphasis was given to in-parallel robotic manipulators.

Mechanical Engineering Journal, Parallel Robotic Manipulators, Robot Arms, Kinematic Chains, Evolutionary Algorithms, Mechanical Errors, Loop Assortments, Link Assortments, Peripheral Loops, Graph Theories.