Mechanism Synthesis Rules

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1 Mechanism Synthesis ules Linkage Transformation ules Grashof s Law Inversion ME312: Dynamics of Mechanisms 1 BB

2 LINKAGE TANSFOMATION ULE 1 evolute joints in any loop can be replaced by prismatic joints with no change in DOF of the mechanism, provided that at least two revolute joints remain in the loop. ME312: Dynamics of Mechanisms 2 BB

3 LINKAGE TANSFOMATION ULE 1: COOLLAY (a) (a) A maximum of two revolute pairs may be replaced by two prism pairs in a given loop of a linkage. No closed link polygon in the chain may have less than two turning pairs ME312: Dynamics of Mechanisms 3 BB

4 LINKAGE TANSFOMATION ULE 1: COOLLAY (b) (b) The axes of substituted prism pairs must intersect one another. No link of the chain may contain only prismatic pairs whose directions of motion are parallel to each other ME312: Dynamics of Mechanisms 4 BB

5 LINKAGE TANSFOMATION ULE 1: COOLLAY (c & d) (c) The axis of the prism pair must be either in the plane of the linkage or in a plane parallel to the plane of the linkage. (d) Binary links of the chain which have only prismatic pair elements may not be directly connected with each other ME312: Dynamics of Mechanisms 5 BB

6 Substituting rism airs in lace of evolute airs ME312: Dynamics of Mechanisms 6 BB

7 Any evolute air can be eplaced by rism airs ME312: Dynamics of Mechanisms 7 BB

8 Substituting a Maximum of 2 rism airs in lace of evolute airs ME312: Dynamics of Mechanisms 8 BB

9 Any 2 evolute airs can be eplaced by 2 rism airs ME312: Dynamics of Mechanisms 9 BB

10 LINKAGE TANSFOMATION ULE 2 Any full joint can be replaced by a half joint, but this will INCEASE the DOF by one. a. A half joint adds an imaginary link and one joint to the system M=0 M=1 L=3 J=3 L=4 J=4 ME312: Dynamics of Mechanisms 10 BB

11 LINKAGE TANSFOMATION ULE 2: COOLLAY (a) A Kinematic Chain with Higher airs can be replaced by an equivalent system of lower pairs. Base oints are at the Center of Curvature Only represents the mechanism in the phase shown Extremely helpful in Velocity Analysis C 23a H 23a H 23b 2 1 C 23b B B ME312: Dynamics of Mechanisms 11 BB

12 LINKAGE TANSFOMATION ULE 2: COOLLAY (b) The centers of curvature of the elements of the higher pairs can be joined together. Base oints are at the Center of Curvature Only represents the mechanism in the phase shown Extremely helpful in Velocity Analysis C 32 2 C 23 C 21a 3 C 21b C 12b C 12a 1 C 13a C 31a 4 B 24 B 26 6 B C 31b B25 B 37 B 38 C 13b 5 B 14 B B 17 B 18 ME312: Dynamics of Mechanisms 12 BB

13 LINKAGE TANSFOMATION ULE 3 Addition of a link will educe the DOF by one, emoval of a link will Increase the DOF by one (the DoF distribution rinciple must be maintained) a. This rule adds one link and two joint to the system Stephenson s Linkage M=+1 ME312: Dynamics of Mechanisms 13 BB

14 LINKAGE TANSFOMATION ULE 4 The Combination of rules 2 and 3 (Addition) above will keep the original DOF unchanged Stephenson s Linkage M=+1 Add Binary Link M=0 M=+1 Turn One Full Joint to a Half Joint M=+1 ME312: Dynamics of Mechanisms 14 BB

15 Simulation of ule 4 Stephenson s Linkage M=+1 Add Binary Link -1 DoF M=0 Turn One Full Joint to a Half Joint +1 DoF M=+1 ME312: Dynamics of Mechanisms 15 BB

16 LINKAGE TANSFOMATION ULE 5 Any ternary or higher-order link can be partially shrunk to a lower-order link by coalescing nodes. This will create a multiple joint but will not change the DOF of the mechanism. artial Shrinkage M=+1 Watt s Linkage M=+1 M=+1 artial Shrinkage ME312: Dynamics of Mechanisms 16 BB

17 LINKAGE TANSFOMATION ULE 6 Complete shrinkage of a higher-order link is equivalent to its removal. A multiple joint will be created, and the DOF will be reduced. Watt s Linkage M=+1 Complete Shrinkage Equivalent to emoval M=0 ME312: Dynamics of Mechanisms 17 BB

18 4 Bar Isomers Can Be Transformed To Other Mechanism Cam airs --B-B --B-B Gear airs --B-B ME312: Dynamics of Mechanisms 18 BB

19 Cam airs (B-B) can be Substituted in lace of evolute airs B B B B ME312: Dynamics of Mechanisms 19 BB

20 Substituting Cam airs in lace of evolute airs B B B B ME312: Dynamics of Mechanisms 20 BB

21 Gear Simulation B B B B ME312: Dynamics of Mechanisms 21 BB

22 ules for Transforming Linkages With Higher Order Elements M L B T Q Designation II Watt s Linkage Stephenson s Linkage 1 2 ME312: Dynamics of Mechanisms 22 BB

23 Substituting a Spring in lace of a evolute air and Two Binary Links ME312: Dynamics of Mechanisms 23 BB

24 Belt and ulley Combinations in lace of evolute airs, Two Binary Links, and a Ternary Link No Slip ME312: Dynamics of Mechanisms 24 BB

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