Universal Journal of Mechanical Engineering 2(1): 1-5, 2014 http://www.hrpub.org DOI: 10.13189/ujme.2014.020101 Rating of Planar Kinematic Chains Using Design Parameters Ashok Dargar Department of Mechanical Engineering, School of Engineering, Sir Padampat Singhania University, NH-76, Udaipur- 313601, India *Corresponding author: dargarashok@rediffmail.com Copyright © 2014 Horizon Research Publishing All rights reserved. Abstract A comparative analysis of kinematic chains and their mechanisms at the conceptual stage of design is essential for the designers. There are large number of distinct chains available in each category, i.e., with specified number of links and degree of freedom. Chains with distinct structures can be expected to posses different characteristics which are not quite obvious. The designer must have some idea about the expected behaviour of the chain at least in comparative sense, so that he can pick up the best chain in order to obtain best performance. To accomplish this, the designer should be able to read the characteristics of the chain based on their topology. Using this belief, in the present work an attempt is made and a method is proposed to compare the chains from the effective utilization of link design parameters, quality of motion and function generation point of view. It provides a simple quantitative estimate to compare all the eligible chains. The concepts developed are applied to planar in- parallel robots, which are gaining in importance. Keywords Kinematic Chain (KC), Chain Link Value, Chain Joint Value, Chain Flow Value 1. Introduction Kinematic chain is a combination of links connected by different kinematic pairs and can be divided into two categories i.e. serial and parallel. Although serial chains have limited choice but in parallel, there are distinct chains are available, such as 16 in eight links single degree of freedom, 40 in nine links 2 degree of freedom, 98 in 10 links 3 degree of freedom and more than 6000 single DOF with twelve links [1, 2]. Therefore complexity of kinematic chains increases with the number of the links of the chains with the same number and type of links. There are no guidelines to select the best possible chain for the specified task such as function generation, path generation or robot manipulator application, despite the availability of many chains with distinct structure. Until now, most of the work is directed to study isomorphism among chains and to know the type of freedom [3-7], work relating to this aspect is hardly seen in the literature. Some work reported earlier [8-10] deals with the dimensional aspects and not with the structural influence. Rao and Rao [11, 12] proposed link-loop Hamming values for rating of the kinematic chains. Rao [13] presented a pseudo genetic algorithm for evaluation of kinematic chains. Rao [14] using the concept of fuzzy logic proposed a numerical measure to compare the chain characteristics like symmetry, parallelism and mobility. Srinath and Rao [15] proposed the concept of correlation to evaluate the performance of the chains. Exact static and dynamic behavior of linkages in an absolute sense cannot be predicted unless the link shapes, dimensions, masses and their distribution etc., are known [16]. However, it should be possible to compare different chains with same number of links and joints for their expected behavior on the basis of their structure, without having to perform the actual static and dynamic analysis. Structure of a chain depends upon the link assortment, i.e., type of link, their number, and their adjacency. Each link is associated with certain number of design parameters. Design parameters are the link lengths, angles etc. which are necessary to form a link. For example a binary link has one design parameter a ternary link has three parameters, a quaternary link has five parameters and a quinternary link has seven design parameters. Performance of a chain depends upon effective use of its design parameters. Selection of the input link or link to be connected to the actuator is important from the point of view of transmission and resolution. In the chain that consist of the same type and number of links the type of joints control the quality of motion generation. So keeping all these aspects of kinematic chains a selection (index) criterion is proposed for kinematic chains from the structural error point of view which provide a simple quantitative estimate to compare all the eligible chains. 2. Definitions of Terminology The following definitions are to be understood clearly