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Sample text
Since only angular movements are concerned, only the three-link length Fig. 3 Kinematic Analysis and Synthesis of Plane Mechanisms 27 ratios (l2/l1), (l3/l1) and (l4/l1) are relevant and should be determined. From Fig. 32b, l23 ¼ ðl1 þ l4 cos h4 À l2 cos h2 Þ2 þ ðl4 sin h4 À l2 sin h2 Þ2 Expanding and then rearranging the terms, the above relation becomes as follows: l1 l1 l2 þ l22 À l23 þ l24 cos h4 À cos h2 þ 1 l2 l4 2l2 l4 ¼ k1 cos h4 À k2 cos h2 þ k3 cosðh2 À h4 Þ ¼ ð1:3:12Þ Now, the synthesized mechanism satisfies the above equation exactly at the specified three positions given by h2 1 , h2 2 and h2 3 with the corresponding values of h4 1 , h4 2 and h4 3 .
The approach is analytical in nature, and this approach is particularly suitable for mechanisms with more than four links. Accuracy point method yields better result if the number of accuracy points is increased and optimally spaced. However, there is a limit to the number of accuracy points. Graphical procedure for motion generation using 4R linkage is demonstrated below with gradually increasing number of accuracy points. 23 shows the basic approach for moving a rigid body for satisfying two positions.
Subsequently, the kinematic pairs are replaced by suitable flexure hinges. e. hinges) only. Fig. 21 Replacement of hinges by flexure joints. a Four-bar mechanism with four hinge joints. b Kinematically equivalent monolithic compliant mechanism 20 1 Introduction Number Synthesis: As mentioned earlier, a mechanism must have appropriate degrees of freedom for proper functioning. If there is only one input motion, then the mechanism must possess a single degree of freedom so that a unique output motion is generated.
