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Problem 1: For the position of the linkage shown, 02 25° All dimensions are in inches. Determine coupler angle, 03 and rocker
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Answer #1

From the figure:

costlcos- l4cos

and

sint sin-4sint0

Substituting given values:

0.72cos2500.68cos0- 0.85cos04= 1.82

0.68cost3 -0.85cos04= 1.167

0.72sin2500.68sin-0.85sin0,= 0

0.68 sint3-0.85sin -0.3043

Solving :

0.68cos3 0.85cos4= 1.167 and 0.68sint3 0.85sin0=-0.3043

This gives the solutions(matlab):

e328.650; 0 = 132.14

03 57.880 04=-161.36

Command Window >>syms q3 q4 0.68* cos (q3) 0.85cos (q4) 1.167 >> e1 0.68 sin (q3) 0.85 sin (q4 >> e2 0.3043 solve (el,e2) [q1

O_2A = 0.72cos25i+0.72sin25j =0.6525i+0.3043j

O2 B 02A+ 0.68cos28.65i0.68sin28.65j 1.2492i + 0.6303

O2P O2A 0.97cos (54 28.65)i0.97sin(54 28.65) 0.7766i 1.2663

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