10.2.3 - Chain Multiplication
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Practice Questions
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What is the purpose of chain multiplication in robotics?
💡 Hint: Think about the relationship between joint movements and end-effector location.
Define what a transformation matrix is.
💡 Hint: Consider how different frames of reference are connected.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is chain multiplication used for in robotics?
💡 Hint: 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.
💡 Hint: Consider what we just discussed about overall transformations.
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Challenge Problems
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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?
💡 Hint: 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?
💡 Hint: Think about how small changes multiply through the chain.
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