CS代考 Task 1 (40%): Get the Jacobian of the three-link manipulator below. As show

Task 1 (40%): Get the Jacobian of the three-link manipulator below. As shown in the figure, all three joints are revolute. Joint 1’s axis is not parallel to the other two. Instead, there is a twist of 90 degrees in magnitude between axes 1 and 2. Write in terms of a frame {4} located at the tip of the hand and having the same orientation as frame {3}. Derive the Jacobian in three different ways: velocity propagation from base to tip, static force propagation from tip to base, and by direct differentiation of the kinematic equations. Compare these three approaches and discuss their pros and cons. 有答案

Task 2 (30%): Construct the dynamic equations for the three-link manipulator in Task 1. Consider each link to be a rectangular solid of homogeneous density with dimensions 𝑙𝑖 , 𝜔𝑖 , and ℎ𝑖 and total mass 𝑚𝑖.

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