Mechanism Fundamentals Number Synthesis • Given a particular DOF determine – Number and order of links • Binary, ternary, quaternary – Number and order of joints • Full joints, half joints, multiple joints Number Synthesis cont. Paradoxes to Gruebler’s • Paradoxes will occur in cases with unique geometry – Must remember to inspect a mechanism during design process for paradoxes • To take advantage of them • To eliminate potential problems they may cause Paradoxes cont. Linkage Isomers • Linkages that have the same – Same number and order of links – Same number of joint – Assembled with different interconnections Are deemed Linkage Isomers Linkage Isomers cont. Linkage Transformation • Modify “revolute only” linkage results from number synthesis Linkage Transformation cont. Brief list of rules that can be applied to Linkage Transformation: 1. Revolute joint can be replaced by prismatic joint w/no change in DOF – Provided at least two revolute joints remain 2. Full joint can be replaced by half joint – Will increase DOF by one 3. Removal of link will reduce DOF by one. Linkage Transformation cont. Linkage Transformation cont. 4. Combination of rules 2 & 3 will keep original DOF 5. Any higher-order link can be partially “shrunk” to a lower-order link by coalescing nodes – Will create a multiple joint – Will not change the DOF of mechanism 6. Complete shrinkage of a higher-link is equivalent to its removal – Will result in a multiple joint – DOF of mechanism will be reduced Linkage Transformation cont. Linkage Transformation cont. Linkage Transformation cont. Kinematic Inversions • Created by grounding a different link in the kinematic chain Kinematic Inversion cont. Kinematic Inversion cont.