MECH368 2022W Midterm solutions

Problem 3: The RPH robot of Figure 3 is shown in its zero position. Determine the end- effector zero position configuration M, and the screw axes S; in {s}. n. F -inta. Sorowo- Zs {s} Xs L₁ ŷs Lo 0₁5 L2 02 {b} zb 103 pitch h = 0.1 m/rad Ấb ŷb L3 Figure 3: An RPH open chain shown at its zero position. All arrows along/about the joint axes are drawn in the positive direction (i.e., in the direction of increasing joint value). The pitch of the screw joint is 0.1 m/rad, i.e., it advances linearly by 0.1 m for every radian rotated. The link lengths are Lo = 4, L₁= 3, L2= 2, and L3= 1 (figure not drawn to scale).

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For the 3-DOF Industrial manipulator arm as shown in Figure 3, determine the joint displacements for known position and orientation of the end of the arm point. 0. 0. Y1A Y2 A Y3 X2 X3 21 22 23 Yo xo Figure 3. 3 DOF RRR Industrial manipulator arm The link transformation matrices are given by C3 -S3 0 a3C3 S3 C3 1 C2 -S2 0 a,C2 C1 S1 -S1 -C1 d1 S2 C2 2T3 %3D T2 1 1 1 1 1 S1 C\C2a3+C1a2 C1C2C3 – C1S2S3 -C¡C2S3 – C1S2S3 S,C2C3 – S1S2S3 -SĄC2S3 – S1 S2C3 -C1 SịC2a3+ Sja2 Szaz + d1 1 OT3 = = °T, 'T2 ?T3 S½C3 + C2S3 - S2S3 + C2C3

For the given Two Link Manipulator (Fig 1), If 11-1m and 12=1m 01-40° and 02-10° Calculate the coordinates of the end effector (x,y)

QUESTION 11 The block diagram of a mechanical transmission system shown in Figure Q11, where K is a positive gain. K (s+20) s(s+1)(s+10) Figure Q11 Its root locus contains two real axis segments. The two segments are: from to to Enter the values as integers, preceded by a - sign if negative, and in increasing order (i.e. going from left to right on the real axis). Example: -20, -15, 7, 19. and from

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منه Ri سے b (1) Starting with the position equation R=Ay, where A is the rotation malux about the 7 oxis and u is a point on the position Vector, derive the velocity equations in both algebraic and matrix foven to solve for Ws and bi What are the vector position and velocity equations? Your motorx equatons must be in the forem: [ ] [ 11 ] = [] [][ b (2) From part 1 device the matrix equation to solve for us and b Wz B = [ w₁] = [ ][ ] b ୧ (3) with the values R₂ = 2in, Rs = 101, R₁ = 8in, Ə₂ = 40°, s = 185' and W₂ = 10 rad/sec B = = [w] Don't forget units Solve w₂ and b. ☐☐ い

The figure below shows an offset slider crank linkage. The links lengths are: link2 = a= 100 mm and link3 = b = 600 mm. The offset is c = 190 mm. we need to : 1. determine the maximum horizontal position of the slider B (dmax) and the corresponding input angle 02 2. determine the minimum horizontal position of the slider B (dmin) and the corresponding input angle 02 Y 03 y В R3 R4 R, 04 R2 02 d ► X R1 The maximum horizontal position of the slider is dmax = Choose... + The input angle 02 corresponding to dmax , in degree and measured CCW from X axis, is = Choose... + The minimum horizontal position of the slider is dmin = Choose... + The input angle 02 corresponding to dmin , in degree and measured CcW from X axis, is = Choose.. +

The simplified robot arm model is given in the following: * = [5 -5 x + |u; y = [03]x 1 Is the system defining the robot arm model observable? O a. Yes O b. No ○ c. Not possible to determine Od. None of the above

Please dont provide solution in an image format thanks

The figure shows a linkage in one position. What is the instantaneous acceleration of point Pif the link O₂A is rotating CW at 40 rad/sec? 4/5 44 201 0₂ Show Transcribed Text MULTIPLE CHOICE a. 8000 in/sec^2 b. 23,073 in/sec^2 c. 15,282 in/sec^2 d. 9,005.8 in/sec^2

Assume the B frame differs from the N frame through a 90 degree rotation about the second N base vector. The corresponding DCM description is: 1 2 3 4 5 6 9 # adjust the return matrix values as needed def result(): dcm = [0, 0, 0, 0, 0, 0, 0, 0, 0] return dcm

Graph about the imagen

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Problem 8-4: Convert (A) 1100111.1101 (binary) into a base 10 number; (B) 4B2F into straight binary; (C) 278.632 (base 10) into straight binary.

QUESTION 1 Consider a 2 DOF system shown below. X1 k₁ m1 F₁ k₂ X2 k3 m₂ F2 The modeshape can be written as (1))] What is x for the second modeshape? Use scientific notation with 3 significant digits and omit units. (eg. -0.123) Let m1 = 2, m2 = 2, k1 = 9, k2 = 8, and k3 = 8.

Given the vectors in Figure P1-2, use a scale of 1 inch = 10 units, and determine the following vectors: Figure P1-2 B=10 ; 270⁰ C=15 ; 210⁰ D=12,5 ; 315⁰ E= 7,5 ; 75⁰ F = 10 ; 215⁰ G= 15 ; 100⁰