Mechanism Fundamentals

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Mechanism Fundamentals
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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

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Number Synthesis cont.
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Paradoxes to Grueblers

• 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

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Paradoxes cont.
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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

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Linkage Isomers cont.
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Linkage Transformation

• Modify revolute only linkage results from
  number synthesis

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Linkage Transformation cont.

• Brief list of rules that can be applied to
  Linkage Transformation
• Revolute joint can be replaced by prismatic joint
  w/no change in DOF
• Provided at least two revolute joints remain
• Full joint can be replaced by half joint
• Will increase DOF by one
• Removal of link will reduce DOF by one.

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Linkage Transformation cont.
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Linkage Transformation cont.

• Combination of rules 2 3 will keep original DOF
• 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
• Complete shrinkage of a higher-link is equivalent
  to its removal
• Will result in a multiple joint
• DOF of mechanism will be reduced

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Linkage Transformation cont.
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Linkage Transformation cont.
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Linkage Transformation cont.
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Kinematic Inversions

• Created by grounding a different link in the
  kinematic chain

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Kinematic Inversion cont.
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Kinematic Inversion cont.