Parallelism in Planar Manipulators: A Measure

Parallelism can be associated with every closed kinematic chain or its representative graph. Parallelism throws light on work space, rigidity, speed ratios (mechanical advantage), etc., and is of great help in selecting multi degree-of-freedom (dof) chains for robotic applications. Numerous distinct chains with the same number of links and dof exist. The extent of parallelism differs from chain to chain and hence a numerical measure is necessary to quantify the same so that the designer gains insight simply based on the structure without having to actually design all the distinct chains before selecting the best chain for the specified task. To the author’s knowledge, no measure is available in graph theory to quantify the extent of parallelism and the present work is an attempt in this direction.