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Day 2.5 - C C which yields both solutions for 2 In many...

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Inverse Kinematics 1/17/2011 21 harder than forward kinematics because there is often more than one possible solution Inverse Kinematics a 1 a 2 x 0 y 0 ( x , y )
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Inverse Kinematics 1/17/2011 22 law of cosines Inverse Kinematics q 2 ? a 1 a 2 x 0 y 0 ( x , y ) 2 2 2 2 1 2 2 2 1 2 ) cos( 2 y x a a a a b q b
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Inverse Kinematics 1/17/2011 23 Inverse Kinematics 2 1 2 2 2 1 2 2 2 2 ) cos( a a a a y x q ) cos( ) cos( 2 2 q q and we have the trigonometric identity 2 2 1 2 2 2 1 2 2 2 2 cos C a a a a y x q therefore, We could take the inverse cosine, but this gives only one of the two solutions.
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Inverse Kinematics 1/17/2011 24 Inverse Kinematics 1 cos sin 2 2 2 q q to obtain Instead, use the two trigonometric identities: q q q cos sin tan
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Unformatted text preview: C C which yields both solutions for 2 . In many programming languages you would use the four quadrant inverse tangent function atan2 c2 = (x*x + y*y – a1*a1 – a2*a2) / (2*a1*a2); s2 = sqrt(1 – c2*c2); theta21 = atan2(s2, c2); theta22 = atan2(-s2, c2); Inverse Kinematics 1/17/2011 25 Exercise for the student: show that Inverse Kinematics 2 2 1 2 2 1 1 1 cos sin tan tan q a a a x y...
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