Mechanism Fundamentals

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					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 number and order of
  – Same number of joint
  – Assembled with different

  Are deemed Linkage
Linkage Isomers cont.
Linkage Transformation
• Modify “revolute only” linkage
  results from number synthesis
     Linkage Transformation
Brief list of rules that can be applied to Linkage

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
     Linkage Transformation
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
Linkage Transformation
Linkage Transformation
    Kinematic Inversions
• Created by grounding a different link
  in the kinematic chain
Kinematic Inversion cont.
Kinematic Inversion cont.