Gure two coordinate frames are dened 0 is attached to

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Unformatted text preview: the 2 ˙ θ2 ˙ θ1 ˙ θ3 z 0 −θ2 1 Ψ0 2 y −θ3 3 z x x θ1 Ψ3 y Figure 3: Robotic mechanism with three links of length 1, three link angles θi , and angular velocities ˙ θi . figure. Two coordinate frames are defined: Ψ0 is attached to the base, Ψ3 is attached to the end of the third link. (a) Prove (by inspection) that the rigid-body transformation from Ψ0 to Ψ3 is given by cos(θ1 + θ2 + θ3 ) − sin(θ1 + θ2 + θ3 ) 0 − sin(θ1 ) − sin(θ1 + θ2 ) − sin(θ1 + θ2 + θ3 ) sin(θ1 + θ2 + θ3 ) cos(θ1 + θ2 + θ3 ) 0 cos(θ1 ) + cos(...
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