Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Textbook Question
Chapter 67, Problem 27A
Find dimension x.
All dimensions are in millimeters
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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…
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Chapter 67 Solutions
Mathematics for Machine Technology
Ch. 67 - Determine the sizes of Aand Bto the nearest...Ch. 67 - Write the cofunction of the complement of the...Ch. 67 - Determine sec 14.8527 rounded to 5 decimal places.Ch. 67 - A steel forging in the shape of a right circular...Ch. 67 - Prob. 5ACh. 67 - The legs of a right triangle are 718 and 912 ....Ch. 67 - Prob. 7ACh. 67 - Prob. 8ACh. 67 - Solve the following exercises. For customary...Ch. 67 - Solve the following exercises. For customary...
Ch. 67 - Solve the following exercises. For customary...Ch. 67 - Solve the following exercises. For customary...Ch. 67 - Solve the following exercises. For customary...Ch. 67 - Solve the following exercises. For customary...Ch. 67 - Find center distance y. All dimensions are in...Ch. 67 - Find inside caliper dimension x. All dimensions...Ch. 67 - Find radius r. All dimensions are in millimeters.Ch. 67 - Find arc dimension x. All dimensions are in...Ch. 67 - Find the depth of cut x. All dimensions are in...Ch. 67 - Find x. All dimensions are in inches.Ch. 67 - Find gage dimension y. All dimensions are in...Ch. 67 - Find y. All dimensions are in inches.Ch. 67 - Find gage dimension x. All dimensions are in...Ch. 67 - Find x. All dimensions are in millimeters.Ch. 67 - Find dimension y. All dimensions are in inches.Ch. 67 - Find y. All dimensions are in inches.Ch. 67 - Find dimension x. All dimensions are in...Ch. 67 - Find x. All dimensions are in inchesCh. 67 - Find distance y. All dimensions are in millimetersCh. 67 - Find dimension y. All dimensions are in inchesCh. 67 - The length L of the point drill with included...
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