Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 2, Problem 2A
Reduce
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Consider a simplified two-joint robotic arm where the two joints are connected by rigid links.Each joint has a mass, and the links are modeled as idealized rods. The motion of each jointaffects the other through the coupling of forces. The system can be modeled by the followingsecond-order coupled ODEs:
m1θ1" + k1(θ1 − θrest) + k3(θ1 − θ2) = 0 (equation 1)m2θ2" + k2(θ2 − θrest) + k3(θ2 − θ1) = 0 (equation 2)
where θ1(t) and θ2(t) represent the angular positions of the first and second joints, respec-tively. m1 and m2 are the effective masses at each joint. k1, k2 and k3 are the stiffnessconstants representing the elastic restoring forces in the joints and links. θrest = 0 representsthe equilibrium position for each joint.The parameters are:m1 = 1, m2 = 1, θrest = 0, k1 = 1, k2 = 2, k3 = 3, θrest = 0The initial conditions are:θ1(0) = 1, θ2(0) = 2Please solve by hand to get θ1(t) and θ2(t) using eigenvectors and eigenvalues. Show all steps/calculations, and provide a written description…
3feet in 1secound; 21feet in x seconds
(15 pts) Show your work to get full credit! Compute a QR factorization of the
matrix
Chapter 2 Solutions
Mathematics for Machine Technology
Ch. 2 - Reduce the fraction 1530to halves.Ch. 2 - Reduce 1230to lowest terms.Ch. 2 - Express 118and ?32as equivalent fractions.Ch. 2 - Express the mixed number 735as an improper...Ch. 2 - Express 9712 as a mixed number.Ch. 2 - Express the mixed number 935as an improper...Ch. 2 - Determine the lowest common denominators of the...Ch. 2 - Determine the lowest common denominators of the...Ch. 2 - Determine the lowest common denominators of the...Ch. 2 - Determine the lowest common denominators of the...
Ch. 2 - Express these fractions as equivalent fractions...Ch. 2 - Express these fractions as equivalent fractions...Ch. 2 - Express these fractions as equivalent fractions...Ch. 2 - Prob. 14ACh. 2 - Prob. 15ACh. 2 - Determine the overall length, width, and height of...Ch. 2 - Determine dimensions A, B, C, D, E, F, and G of...Ch. 2 - Determine dimensions A, B, C, and D of pin in...Ch. 2 - The operation sheet for machining an aluminum...
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