How Does the Jacobian Process Work in Kinematics?

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clurt
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Hey guys,

Im studying for an exam and don't fully understand the jacobian process. Speciffically how you can differential the middle colum with respect to theta_3. Please view attached. So from step 1 to 2. Thanks.
 
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  • Handwritten notes on lined paper: a position vector q with components r1, r2, r3 and the constraint r1 + r2 - r3 = 0, followed by a forward kinematics x and y expression in cos and sin of theta 1, theta 2 and theta 3, then a Jacobian matrix with entries cos theta 1, -cos theta 2 and sin theta 1, -sin theta 2, plus r3 terms.
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