Structural Synthesis of Planar Kinematic Chains and Their Detection of Isomorphism

• Published in: Journal of the Institution of Engineers (India) Series C Vol. 105; no. 1; pp. 141 - 159
• Main Authors: Ahamad, Sayeed, Khan, Sabah, Mohammad, Aas
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.02.2024; Springer Nature B.V
• Subjects: Aerospace Technology and Astronautics; Beverage cans; Beverages; Chains; Degrees of freedom; Design analysis; Design optimization; Engineering; Industrial and Production Engineering; Isomorphism; Kinematics; Linkages; Mechanical Engineering; Movement; Original Contribution; Polynomials; Slider-crank mechanisms; Synthesis; Walking machines; Isomorphism; Kinematic chains; SCJVM and transformed adjacency matrix; Kinematic pairs
• ISSN: 2250-0545; 2250-0553
• DOI: 10.1007/s40032-023-01012-0

Design is the building of synthesized solutions with appearance of component or systems that propitiate customer’s necessity. When we are disposed a design problem, we effort to make the better utilization of our notion and the present facts are to declare problem and develop as several practicable explanation as possible. Now, we estimate the ideas against the client’s necessities and select a most favourable opinion for design analysis, synthesis and design optimization. Different methods are introduced by apart authors for discernment of isomorphism of planar kinematic chains. So everybody has detected that some obstacles to get new issues. In this paper, a bid has been built up which give the recognizance of isomorphism of kinematic chains utilizing distinct revolute joints, to think about carefully examples of slider crank mechanism (Beverage can crusher) and Rear-window wiper mechanism (four bar mechanism), Planar 1 degree of freedom, six bar linkages (Watt’s Chain), Planar 1 degree of freedom, six bar linkages (Stephenson’s Chain) and Planar single (or one) degree of freedom, Eight bar linkages. By applying link-link type of transformed matrix [TM] and components of matrix was marked as 1 and 0 which is depend upon the presence or absence of a relation in between the revolute joints. To reduce this problem, we make an effort to improve desperate set of matrix called Sum of Cube of Joint Value Matrix (SCJVM). In this paper, an approach based on Bocher’s formula is presented to identify all isomorphism and distinct Mechanisms with different links and test for two degrees of freedom. The suggested method is utilized for computing the characteristic or peculiarity polynomial expressions of their mechanisms and to examining (Beverage can crusher) and Rear-window wiper mechanism, six bar linkages (Watt’s Chain), six bar linkages Stephenson’s Chain. Applications of present work are four bar kinematic chains are back-and-forth movement of the rider’s legs gets transformed into circular motion through a four-bar linkage system comprised of the two leg parts, the bike frame, and the crank. Six bar kinematic chains such as “Klann linkage”, are employed to create to the legs of walking machine.