Rose-Hulman ES 204 - ES 204 Lab 3 (3 pages)

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ES 204 Lab 3



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ES 204 Lab 3

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3
School:
Rose-Hulman Institute of Technology
Course:
Es 204 - Mechanical Systems
Mechanical Systems Documents
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Rose Hulman Institute of Technology Department of Mechanical Engineering ES 204 Mechanical Systems ES204 Mechanical Systems Working Model Lab 03 Precise payload positioning by an overhead crane especially when performed by an operator using only visual feedback to position the payload is difficult due to the fact that the payload can exhibit a pendulum like swinging motion In this lab we experimentally investigate the overhead crane model pendulum and simulate its motion using Working Model In this portion of the lab you will compare in a simulation the final angular velocity of rods with weights attached that demonstrate general plane motion Try to predict the best location of the moveable mass such that residual oscillations are zero after the trolley moves You will be able to understand the overhead crane problem a bit better and you will use the model to help predict the behavior of the hardware experiment At the same time you will increase your ability to use Working Model You will analyze this problem in homework for day 25 problem 4 48 using principles that you have learned in ES204 You will be required to use this information to predict the behavior of the swinging rod device and to compare your analytical solution to your Working Model solution Your final Working Model should look like the following Working Model Instructions Be sure the units you are using are SI and radians View Numbers and Units It is often convenient to turn on a rulers grid and axes View Workspace 1 Set the mass unit to grams and the length unit to centimeters View Numbers and Units more choices 2 Set view size window width to 230 cm View View Size 3 Create a rectangle that is 43 2 cm tall by 1 5 cm wide height 43 2 width 1 5 and has mass equal to 68 5g 4 Create a horizontal slot element that will serve as the crane track 5 Place a round point element at the top of the rectangle Select both the round point element and the slot element shift click and then click Join 6 Modify the equation for the pin to move it down half the radius of the sensor for the rod Double click on the pin and modify the formula for the y location to be body height 2 0 1 25 where simply is the object number of the rod 7 Create a circular object of radius 2 5 cm to act as an adjustable weight Place a square point element in the center of the circle 8 Place a square point element in the middle of the rod and while the point element is highlighted create a slider control by choosing Define New Control Offset Delete the x offset control Double click on the word yoffset and set the min and max values to 0 and 40 9 Select the square point element and change the y equation from Input to 43 2 21 25 Input When the offset is set to zero the disk should be at the pin location of the pendulum 10 Highlight the two square point elements using shift click and then click on JOIN 11 Set the adjustable mass weight to 88g 12 Create a meter to measure the angular velocity of the bar Highlight the rod choose Measure Velocity Rotational Graph Click twice on the white arrow in the upper left of the meter and you will have a digital meter rather than a graph Set the y1 minimum to 1 and the maximum to 1 and the x minimum to 0 and the maximum to 2 5 Be sure to deselect the auto checkboxes 13 Add two actuators anchored to the background and the round pin element at the top of the rod You may need to zoom in to be sure you select the pin in the slot as one end of the actuator Open the actuator properties window and change the type to Acceleration then type in the equation 100 000 0 018952 43 5668 2 exp 43 5668 time 0 2153 exp 43 5668 time0 2153 1 1 exp 43 5668 time 0 2153 3 Change the Active When to time 0 5 For the second actuator the equation is 100 000 0 018952 43 5668 2 exp 43 5668 time 0 7153 exp 43 5668 time0 7153 1 1 exp 43 5668 time 0 7153 3 Change the Active When to time 0 5 Your should have a simulation that now works with a double move For convenience we are going to have two different working model files one for a single move and one for a double move Be sure to save the work you have done so far with a filename such as crane double move wm2d For a single move strategy let s save this file with a different name such as crane single move Once you have a file for the single move delete the second actuator and double the magnitude of the first prescribed acceleration 200 000 0 018952 43 5668 2 exp 43 5668 time 0 2153 exp 43 5668 time0 2153 1 1 exp 43 5668 time 0 2153 3 Change the Active When to Always Test the eight configurations represented by Lwcg d s 2 n 1 2 dw n 1 2 K 8 Where Sensor diameter d s 2 5 cm moveable weight diameter d w 5 cm Try both the single and double move strategies for each configuration Use the Excel spreadsheet sent to you to record your numbers To find the angular velocity scroll the time to a peak after the actuators stop and then turn the graph into a meter Finally use trial and error to find the ideal mass location to reduce the angular velocity of the rod Figure 1 taken from Y Fang W E Dixon D M Dawson and E Zergeroglu Nonlinear Coupling Control Laws for an Underactuated Overhead Crane System IEEE ASME Transactions on Mechatronics Vol 8 No 3 September 2003


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