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6-8 Consider a 3-link Cartesian manipulator, (a) Compute the inertia tensor J; for each link i = 1, 2, 3 assuming that the links are uniform rectan- gular solids of length 1, width 1/4, height 1/4, and mass 1. (note these are all unitless!) (b) Compute the 3 x 3 inertia matrix D(q) for this manipulator (c) Show that the Christoffel symbols Cijk are all zero for this robot. Interpret the menaing of this for the dynamic equations of motion. (d) Derive the equations of motion in matrix form: D(q) + C(q, q)ġ + g(q) = U

6-8 Consider a 3-link Cartesian manipulator, (a) Compute the inertia tensor J; for each link i = 1, 2, 3 assuming that the links are uniform rectan- gular solids of length 1, width 1/4, height 1/4, and mass 1. (note these are all unitless!) (b) Compute the 3 x 3 inertia matrix D(q) for this manipulator (c) Show that the Christoffel symbols Cijk are all zero for this robot. Interpret the menaing of this for the dynamic equations of motion. (d) Derive the equations of motion in matrix form: D(q) + C(q, q)ġ + g(q) = U

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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6-8 Consider a 3-link Cartesian manipulator, (a) Compute the inertia tensor J₁ for each link i = 1, 2, 3 assuming that the links are uniform rectan- gular solids of length 1, width 1/4, height 1/4, and mass 1. (note these are all unitless!) (b) Compute the 3 × 3 inertia matrix D(q) for this manipulator (c) Show that the Christoffel symbols Cijk are all zero for this robot. Interpret the menaing of this for the dynamic equations of motion. (d) Derive the equations of motion in matrix form: D(q) + C(q, q) q + g(q) = u
Transcribed Image Text:6-8 Consider a 3-link Cartesian manipulator, (a) Compute the inertia tensor J₁ for each link i = 1, 2, 3 assuming that the links are uniform rectan- gular solids of length 1, width 1/4, height 1/4, and mass 1. (note these are all unitless!) (b) Compute the 3 × 3 inertia matrix D(q) for this manipulator (c) Show that the Christoffel symbols Cijk are all zero for this robot. Interpret the menaing of this for the dynamic equations of motion. (d) Derive the equations of motion in matrix form: D(q) + C(q, q) q + g(q) = u
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