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 kinematic equations for H3 based on the answer in a).
(0.5 marks)
c) Solve the forward kinematics problem using the following input data:
L₁=2, L2=1, L3= 0.5 (m), = {01, 02, 03}T, assume 0₁<10, 15<0₂<50, and 03<0.
(1 marks)
d) Check your result in c) by sketching the robot configuration.
(1 marks)
23
or iz
The coordinate systems of the three-link planar arm
Fig: 1
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.)
A 220 V, three-phase, 6-pole, 60 Hz induction motor is running at a slip of 2.5%, and delivers5 kW to its load. The rotational losses are 500 W. Find O The speed of rotation magnetic field produced by the stator in rps; The speed of rotation magnetic field produced by the rotor in rps; The frequency of the voltage induced in the rotor; The slip speed in rps; The mechanical speed of the rotor in rpm; The load torque; 2) The converted power; The airgap power; ) The induced torque; The rotor copper losses.
7.) A small permanent magnet motor has a torque constant kr=0.1 Nm/A and a back e.m.f.constant ke-2.50 V/krpm. The total internal resistance is R=15 2. Determine the torque for maximum power and the maximum rotational speed if the applied voltage is V=5V. (25pts)
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.
In El 02.04, which of the follow is the time constant? \text { a. } \frac{R_{1}}{L}+\frac{R_{2}}{L} \text { b. } \frac{L}{R_{1}}+\frac{L}{R_{2}} \text { c. } \frac{1}{R_{1}}+\frac{1}{R_{2}} \text { d. } \frac{L R_{2}}{R_{1}}+\frac{L R_{1}}{R_{2}}
In El 02.03, which of the following is the root of the characteristic equation (used for the homogeneous solution)? \text { a. } \frac{-R}{C} \text { b. } \frac{-1}{C} \text { C. } \frac{G}{R} \text { d. } \frac{-1}{17 C} \text { e. } \frac{-1}{R}
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. Consider frames {0}, {1} and {2} shown below. Assume that no rotation is allowed around Y axis and the maximum angle each axis can rotate at each time is 90 degrees. a. Find the homogeneous transformation matrices ⓇH, and¹H₂. b. Find H, using the relationship: "H₂="H,¹H₂. Z₁4 1m 1m Z₁ Z₂ Assume positive or negative rotations about the axes. You must write the transformation equations.