Linkage_Synthesis_-_3_precision_points

Linkage_Synthesis_-_3_precision_points - Three-Position...

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Unformatted text preview: Three-Position Motion Generation By Analytical Synthesis Three-Position Analytical Synthesis Vector Loop Closures (LHS): 1 1 21 2 2 W Z P Z W ( loop ) 2 1 1 2 2 2 O A P P A O 1 1 31 3 3 W Z P Z W ( loop ) 2 1 1 3 3 2 O A P P A O The above two vector equations can be written as: 2 2 2 21 j j j j j e w e z e p e z e w 3 3 3 31 j j j j j e w e z e p e z e w Setting: , etc. and simplifying: 2 2 . j j j e e e 2 2 2 21 1 1 j j j j j e p e e z e e w 3 3 3 31 1 1 j j j j j e p e e z e e w Three-Position Analytical Synthesis (contd) Applying Eulers identity: , etc. and simplifying: sin cos j e j 2 21 2 2 2 2 cos sin sin 1 cos cos sin sin 1 cos cos p z z w w EQ. (1) 3 31 3 3 3 3 cos sin sin 1 cos cos sin sin 1 cos cos p z z w w EQ. (2) Real Part: 2 21 2 2 2 2 sin sin cos 1 cos sin sin cos 1 cos sin...
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Linkage_Synthesis_-_3_precision_points - Three-Position...

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