2. 3 → 1 → 2 rotation sequence, with corresponding angles of α, ẞ, and y is considered. a. Find the transformation matrix between the frames. b. Relate the Euler angle rates and angular velocities measured in the new frame.

If the coordinate frame 0₁x₁Y₁Z₁ is obtained from the coordinate frame ooxoyoZo by a rotation of π/2 about the x-axis followed by a rotation π/3 about the fixed y -axis, calculate the rotation matrix R representing the composite transformation. Sketch the initial and final frame. R F F4 Q Search DII % 5 FS T G Y PRE * H & 7 99+ PrtScn FB S Home End F10

pay attention to the allow and F2 direction on 2a

Find a vector x whose image under T, defined by T(x) = Ax, is b, and determine whether x is unique. Let 1 3 6 15 4 15 27 69 0 1 1 -4 - 13 - 25 A= b= x= 3 - 63 Find a single vector x whose image under T is b. s the vector x found in the previous step unique? O A. Yes, because there are no free variables in the system of equations. O B. Yes, because there is a free variable in the system of equations. O C. No, because there are no free variables in the system of equations. O D. No, because there is a free variable in the system of equations.

I am struggling coming up with the equation to solve this.

Determine the rotation matrix for a rotation of 450 about y -axis, followed by a rotation of 120 about z-axis, and a final rotation of 900 about x-axis

I want a detailed explanation of the two areas marked in red. Firstly, why + and - became in derivation all - Secondly, why did we put it above C dot and why did we delete a? I want an explanation about this derivation with a detailed explanation of its drawing, please.

Please help me

For the walking-beam mechanism shown in Figure 3, find and plot the x and y coordinates of the position of the coupler point P for one complete revolution of the crank O2A. Use the coordinate system shown in Figure 3. Hint: Calculate them first with respect to the ground link 0204 and then transform them into the global XY coordinate system. y -1.75 Ꮎ Ꮎ 4 = 2.33 0242.22 L4 x AP = 3.06 L2 = 1.0 W2 31° B 03 L3 = 2.06 P 1 8 5 .06 6 7 P'

For the 3Bar Inverted Crank Slider shown, the following data is given: R2 = a, R₁ =d, 02, W2, α2. απ W2 R2 02 02 R4 04 O2 and 04 are grounds. 04 R1 1. Starting with the algebraic position equation R = Au; where R is the position of the vector in the fixed frame [XY]T, A is the rotation matrix and u is the coordinates of a point on the vector in the local frame, [xy]. With R₂ = a, R₁ = d, 02, W2, and a₂ given, derive the general position, velocity, and acceleration equations in both algebraic and matrix form. Note: your answer must begin with the vector loop and continue the derivation. 2. For the 3-bar crank slider with R2 = 2 in, R₁ =10 in, 02 = 20°, w₂ = 10 rad/sec ccw, α₂ = 0 rad/sec², determine values for R4 = c, 04, Ċ, W4, C, and α. 3. What are the angular velocity and acceleration for the slider block.