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Home Explore Fundamentals of robotic mechanical systems_ theory, methods, and algorithms-Springer (2003)

Fundamentals of robotic mechanical systems_ theory, methods, and algorithms-Springer (2003)

Published by Willington Island, 2021-07-03 02:58:54

Description: Modern robotics dates from the late 1960s, when progress in the development of microprocessors made possible the computer control of a multiaxial manipulator. Since then, robotics has evolved to connect with many branches of science and engineering, and to encompass such diverse fields as computer vision, artificial intelligence, and speech recognition. This book deals with robots - such as remote manipulators, multifingered hands, walking machines, flight simulators, and machine tools - that rely on mechanical systems to perform their tasks. It aims to establish the foundations on which the design, control and implementation of the underlying mechanical systems are based. The treatment assumes familiarity with some calculus, linear algebra, and elementary mechanics; however, the elements of rigid-body mechanics and of linear transformations are reviewed in the first chapters, making the presentation self-contained. An extensive set of exercises is included. Topics covered include: kin

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158 4. Kinetostatics of Simple Robotic Manipulators represented in the same coordinate frame, say, the first one. We then have the expansion below: J˙ θ˙ = θ˙1 0 + θ˙2 e˙ 2 + · · · + θ˙n e˙ n (4.92) u˙ 1 u˙ 2 u˙ n The right-hand side of eq.(4.92) is computed recursively as described below in five steps, the number of operations required being included at the end of each step. 1. Compute { [ ωi ]i }1n: [ ω1 ]1 ← θ˙1[ e1 ]1 For i = 1 to n − 1 do [ ωi+1 ]i+1 ← θ˙i+1[ ei+1 ]i+1 + QTi [ ωi ]i enddo 8(n − 1) M & 5(n − 1) A 2. Compute { [ e˙ i ]i }1n: 0M & 0A [ e˙ 1 ]1 ← [ 0 ]1 For i = 2 to n do [ e˙ i ]i ← [ ωi × ei ]i enddo 3. Compute { [ r˙ i ]i }1n: [ r˙ n ]n ← [ ωn × an ]n For i = n − 1 to 1 do [ r˙ i ]i ← [ ωi × ai ]i + Qi[ r˙ i+1 ]i+1 enddo (14n − 8)M & (10n − 7)A 4. Compute { [ u˙ i ]i }n1 using the expression appearing in eq.(4.89c): [ u˙ 1 ]1 ← [ e1 × r˙ 1 ]1 For i = 2 to n do [ u˙ i ]i ← [ e˙ i × ri + ei × r˙i ]i enddo 4(n − 1) M & 3(n − 1) A TLFeBOOK


































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