The serial manipulator shown in figure 1 (in the attachment) is set in a configuration such that the pose of the effector with respect to a world reference frame, Rworld, is defined by the composed homogeneous transformation matrix, Qgripper/world, that follows (defined with respect to evolving reference frames):

{Please refer to the attachment for the matrix.}

On the other hand, the pose of the robot base with respect to the world reference frame, Rworld, is defined by the composed homogeneous transformation matrix, Qbase/world, that follows (defined with respect to evolving reference frames):

{Please refer to the attachment for the matrix.}

Moreover, the Denavit-Hartenberg parameters of the manipulator in this configuration are defined as follows:

{Please refer to the attachment for the table.}

Determine the rotation angle of the second degree of freedom, theta2, that must be used to bring the effector to the specified configuration.

A wheel accelerates with a constant angular acceleration of 4.5 rad/s^2. If the initial angular velocity is 1.0 rad/s, what is theangle through which the wheel rotates in 2.0 s?
Please provide detailed explanation.

Given the 2x2 matrices A, B, and C (active transformation matrices) in the x, y plane do the following:
(A, B and C are 2x2 matrices given below)
1. Show the matrix is orthogonal
2. Find the determinant to indicate if a rotation or reflection matrix
3. Find therotationangle or find the line of reflection.
A= 1/(2)

In terms of radians and X, what would be the specifications of the anlges for trigonometric points which result from the following transformations of the trigonometric point P(X)? (Work these out on a diagram of the unit circle)
1) A reflection y = x followed by a rotation through pi
2) A reflection in y = -x
3) A refle

We use matrices, eigenvalues and eigenvectors to solve the following:
Let f be therotation in the 3-dimensional space about the x-axis through theangle pi/2 and g be therotation about the y-axis through the same angle. Describe therotation f g. Let h be the reflection in the plane orthogonal
to the vector 2i - j + 3k. D

In an amusement park rocket ride, cars are suspended from L = 4.17-m cables attached to rotating arms at a distance of
d = 6.15 m from the axis of rotation. The cables swing out at an angle of _ = 46.2_ when the ride is operating. What is
the angular speed of rotation? (File is attached below)

Write an inequality in the variable x for thedegree measure of the smallest angle of a triangle given that thedegree measure of the smallest angle is at most 30 degrees
diagram
top angle x+8
bottom left x
right angle has ?

A projectile of mass m is fired from the surface of the earth at an angle A from the vertical. The initial speed Vo is equal to the square root (GMe/Re). How high does the projectile rise? Neglect air resistance and the earth's rotation. (Hint: It is probably easier to apply the conservation laws directly instead of using orbit

Two solid steel shafts (G = 11.2 x 106 psi) are connected by the gears shown. Ends B and D are fixed. Assume points A and C are where the gears meets the shafts.
What is the maximum shear stress in shaft CD under the loading shown?
Choose One: 7.832ksi 6.987ksi 6.443ksi 5.844ksi
What is theangle through which end C r