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2 cards from this section. Quick, good the night before a test.
What is the purpose of chain multiplication in robotics?
Think about the relationship between joint movements and end-effector location.
Define what a transformation matrix is.
Consider how different frames of reference are connected.
What is chain multiplication used for in robotics?
Think about the impact of joint movement on the end result.
True or False: Chain multiplication can yield the overall transformation of a robot's end-effector.
Consider what we just discussed about overall transformations.
A robotic manipulator uses chain multiplication to compute the final position of its end-effector. If the transformation matrices due to three joints are given as T1, T2, and T3, and their values are: T1 = [[1, 0, 0, 2], [0, 1, 0, 3], [0, 0, 1, 1], [0, 0, 0, 1]], T2 = [[0, -1, 0, 1], [1, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]], T3 = [[1, 0, 0, 2], [0, 1, 0, 1], [0, 0, 1, 3], [0, 0, 0, 1]]. Calculate the overall transformation matrix T = T1 * T2 * T3. What is the resultant T matrix?
Take it step by step; multiply the matrices two at a time.
If errors occur in the transformation matrices by ±0.1 in each element, discuss how this would affect the position of the end-effector. Would the overall transformation still be reliable?
Think about how small changes multiply through the chain.
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