5.) A force of 500 N is required to open a process control valve. What area of diaphragm will be needed with a diaphragm actuator to open the valve with a control gauge pressure of 70 kPa? (20 pts)

2.) Consider a Pt resistance sensor that requires long leads to operate. To compensate for the changes in the resistance of long leads, the sensor can be connected to a Wheatstone bridge (as R1, see picture) using long leads (1,2,3) of same dimensions and material. They will all be subject to the same change in resistance (AR) due to temperature. If we consider lead #1 in series with R3 and lead #3 in series with R1, for R1 = R3 (and hence R2 = R4),starting from the general Wheatstone bridge output expression: \mathbf{V}_{\bullet}=\mathbf{V}_{\mathbf{A B}}-\mathbf{V}_{\mathbf{A D}}=\mathbf{V}_{\mathbf{2}}\left(\frac{\mathbf{R}_{\mathbf{1}}}{\mathbf{R}_{\mathbf{1}}+\mathbf{R}_{\mathbf{2}}}-\frac{\mathbf{R}_{\mathbf{3}}}{\mathbf{R}_{\mathbf{3}}+\mathbf{R}_{\mathbf{4}}}\right) show that the Wheatstone bridge cancels the effects of temperature on the long leads. In other words, show that V. = 0 when temperature varies and affects the resistance of the long leads.

3.) A diaphragm pressure gauge employs four strain gauges to monitor the displacement of the diaphragm. The four active gauges form the arms of a Wheatstone bridge, in the way shown in Fig. 3.23 b (see class notes too). The gauges have a gauge factor of 2.1 and resistance 120 Q. A differential pressure applied to the diaphragm results in two of the gauges on one side of the diaphragm being subject to a tensile strain of 1.0 x 10^-5 and the two on the other side a compressive strain of 1.0 x 10^-5 . The supply voltage for the bridge is 10 V. What will be the voltage output from the bridge? (20 pts) (Answer is 0.21 mV, but you need to show the work to get to this.)

2. This is a 3 DOF planar robot with 3 rotational joints. Derive the transformation matrix between the end-effector and the base of the robot coordinate systems. Assume the y and z axes orientations at every joint (y axis is given) and draw your assumptions in the free body diagram. Your assumptions will vary from your fellow students, if there is an intentional match both parties will receive zero marks! (a) DH (b) Three-link, nonplanar manipulator.

4. As shown in the following figure, it is an ABB IRB140 industrial robot. It has six DOF and all the major dimensions are given. The last three axes intersect with each other and have the common origin located at the centre of axis 5. Please derive the transformation matrix between the end-effector (6) and the base of the robot coordinates systems {0} using the homogenous transformation method. Assume the axes orientations at every joint and draw your assumptions in the free body diagram. Your assumptions will vary from your fellow students, if there is an intentional match both parties will receive zero marks! The link lengths are given in the diagram. You may use MATLAB for matrix multiplications. 670 Te 70 380 65 810 486 1092 712 352 151

A 208V Y-connected synchronous motor is drawing 50 A at unity power factor from a 208Vpower system. The field current flowing under these conditions is 2.7 A. Its synchronous reactance is 1.6 N. Assume a linear open-circuit characteristic. Find V, and E, for these conditions.'A Find the torque angle ð. What is the static stability power limit under these conditions? O How much field current would be required to make the motor operate at 0.80 PF leading? What is the new torque angle in part (d)?

3. This is a 3 DOF spatial robot with 2 rotational joints and 1 translational joint in the reference pose. [3 marks] Yo dz Please answer the follow questions using the DH method: a) Define all the required coordinate systems associated with each joint and derive link parameters based on the DH method. [y-axis direction is given; you have to assume the other axes directions] (0.5 mark) b) Derive the transformation matrix between the end-effector and the base coordinate system ³Ho. (1.5 mark) c) Calculate the coordinates of the point C and draw the corresponding configurations based on the values of parameters and variables given: 1₁ = 12 = 13= 6, 0₁-30°, 0₂ = 60° and assume d3 (1 marks).

In El 02.02, which of the following is the capacitor voltage? Let T be the time constant.Select \text { a. } k e^{-t / \tau}+K_{1} e^{-t / \tau} \text { cos(wt) }+r \text { b. }\left(v_{C 0}-R A_{n}\right) e^{-t / \tau}+R_{A} \text { c. } v_{C 0} e^{-t / \tau}+R A_{0} \text { d. }\left(v_{C 0}-R A_{0}\right) e^{-t / T} \text { e. } v_{C 0} e^{-t / \tau}+A_{0}

1. For the arm with three degrees of freedom shown in the figure, please answer all the questions below: [4 marks] yo L₁ L3 8₂ a) Define all the required coordinate systems associated with each joint based on the DH method. [y-axis direction is given; you have to assume the other axes directions] (0.5 mark) b) Derive link parameters based on the answer in a). (DH method!) (0.5 marks) c) Derive the kinematic equations for ³Ho based on the answer in b). (1.5 marks) d) Solve the forward kinematics problem using the following input data: L₁ = 4, L₂ = 2, L3= 1 (m), and Ⓒ = {0₁, 0₂, 03}¹ = {——,——‚— —} assume the numerical values of the angles less than 90 degrees. (1 mark) e) Check your result in d) by sketching the robot configuration as a line diagram to represent robot links. (0.5 marks).

1. Find out the homogeneous transformation matrices to describing the pose of the Oo frame with respect to the frame 03. Assume the axes orientations at O₁, O2 and O3 any combination other than in Lecture 4 PDF file (week 4 & 5), slides 24 & 25. Consider O:(x0,0,zo), assume the values of xo and zo. Similarly, assume the O₂ and O3 axes scaling as per the xo and zo initially assumed values. Your assumptions will vary from your fellow students, if there is an intentional match both parties will receive zero marks! 0₁