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aa2_intro

# aa2_intro - Mechanisms vs Structures If an assembly of...

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1 Mechanisms vs. Structures If an assembly of interconnected links has M > 0 Æ Mechanism M = 0 Æ Structure M < 0 Æ in-determinate or overly constrained structure

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2 Number Synthesis ± Definition of number synthesis The determination of number and order of links and joints necessary to produce motion of a given DOF. ± Link order Nodes per link – binary, ternary, etc. ± Purpose Allows an exhaustive determination of all possible combinations of links that will yield a chosen M.
3 Hypothesis (theorem) ± If all joints are full joints (J) (revolute or prismatic), then odd M requires even L, and vice versa. { { even even is L if odd odd is L if even even minus odd if odd even minus even if even 2 ) 1 ( 3 J L M = 3 2 1

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4 General Equations ± Notations: B for number of binary links,T for ternary,Q for quaternary,P for pentagonal,H for hexagonal. ± Basic Equations J L M 2 ) 1 ( 3 = H P Q T B L + + + + = ( ) 2 6 5 4 3 2 H P Q T B J + + + + =
5 From the 2 nd equation: 2L =2B+2T+2Q+2P+2H From the 3 rd equation: 2J = 2B+3T+4Q+5P+6H Æ

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aa2_intro - Mechanisms vs Structures If an assembly of...

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