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d₂ L 다. de I Revolute 8 Prismatic TIITT
With the robot in Figure 1 we are interested in achieving a task involving the transfer of parts between conveyor belts and brief interaction with a human. Specifically. imagine that there are two conveyor belts, one on either side of the robot (i.e., one located in the direction out of the page, the other located in the direction into the page). From the first conveyor belt (out of the page), the robot grasps a part and transfers it to a point farther down the second conveyor belt into the page, farther to the right than the initial grasping point). During this transfer operation, the robot must ensure that it can safely allow a human to insert a delicate portion of the part before transfer to the second conveyor belt. In the described application context, solve the following problems (NOTE: *You* are in control of any unspecified parameters and/or constraints necessary to solve the problems): (a) Design 3 path points (desired end effector poses) that can achieve the described transfer operation under the following constraints: the end effector must be positioned above the first conveyor belt and oriented towards the bottom of the page during the initial grasping operation; the end effector must be positioned between the two conveyor belts and must be rotated 90 degrees relative to the initial grasping operation during the human interaction; and the end effector must be positioned above the second conveyor belt and rotated 45 degrees relative to the human interaction during the part drop off. (b) Design a smooth polynomial function to describe each desired joint variable for the robot to achieve the desired path points from part (a) and plot these functions. The polynomials must be designed such that constraints on joint velocity *and* acceleration can be specified, and it must be ensured that during the human interaction the angular velocity of the end effector (relative to the end effector frame) does not exceed 1 rad/s and the angular acceleration of the end effector (relative to the end effector frame) does not exceed 0.5 rad/s2. You *MUST* show your work for deriving the polynomials,