Estimated student time to complete: minutes Prerequisite knowledge required: Text Section s 2. Express the vector in matrix form. If not, find the necessary unit vector s to form a frame between p, q, and s. However, p and q are perpendicular to each other, and we can select s to be perpendicular to those two. Of course, p is not a unit length, therefore we use the unit vector representing it.
Find the new location of the point relative to the reference frame. T Estimated student time to complete: 5 minutes Prerequisite knowledge required: Text Section s 2. Find the new location of T the frame relative to the reference frame.
Related Papers. By Carl V Lewis. By Casen Xu. Estimated student time to complete: minutes if Problem 2. What is the effect of a differential rotation of 0. Find the new location of the hand. What is the differential operator relative to the reference frame? What is the differential operator relative to the frame A? Find a transformation matrix Q that will accomplish this transform in the Universe frame. By inspection, find a differential translation and a differential rotation that constitute this operator.
The corresponding inverse Jacobian of the robot at this location is also given. The robot makes a differential motion, as a result of which, the change in the frame dT is recorded as given. Find the new location of the camera after the differential motion.
Find the differential operator. Find the joint differential motion values associated with this move. Find how much the differential motions of the hand-frame T D should have been instead, if measured relative to frame T, to move the robot to the same new location as in part a. The corresponding inverse Jacobian of the robot relative to the frame at this location is also given. The robot makes a differential motion, as a result of which, the change dT in the frame is recorded as given.
The corresponding inverse Jacobian of the robot at this location relative to this frame is also shown. Find which joints must make a differential motion, and by how much, in order to create the indicated differential motions. Find the change in the frame. Find the new location of the frame after the differential motion. Find how much the differential motions given above should have been if measured relative to the Universe, to move the robot to the same new location as in Part c.
The corresponding inverse Jacobian of the robot at this location is also shown. Find how much the differential motions given above should have been, if measured relative to Frame T, to move the robot to the same new location as in Part c.
Estimated student time to complete: 20 minutes Prerequisite knowledge required: Text Section s 3. From Equation 3. Estimated student time to complete: 10 minutes Prerequisite knowledge required: Text Section s 3. Find the three components of the velocity of the hand frame. Estimated student time to complete: 10 or 20 minutes Prerequisite knowledge required: Text Section s 3.
Find the required three joint velocities that will generate the given hand frame velocity. Kinematic: First we write equations describing the kinematic relationships. Estimated student time to complete: 30 minutes Prerequisite knowledge required: Text Section s 4. Estimated student time to complete: minutes Prerequisite knowledge required: Text Section s 4. Di terms are gravity terms. Estimated student time to complete: 1 hour Prerequisite knowledge required: Text Section s 4.
From Equation 4. Attached to the object is a frame, which describes the orientation and the location of the object. Find the equivalent forces and torques acting on the object relative to the current frame. Assuming that the two parts must be aligned together for this purpose, find the necessary forces and moments that the robot must apply to the part relative to its hand frame. Calculate the coefficients for a third-order polynomial joint-space trajectory.
Determine the joint angles, velocities, and accelerations at 1, 2, and 3 seconds. It is assumed that the robot starts from rest, and stops at its destination. Estimated student time to complete: minutes Prerequisite knowledge required: Text Section s 5.
Calculate the coefficients for a third-order polynomial joint-space trajectory and plot the joint angles, velocities, and accelerations. Estimated student time to complete: minutes with plotting Prerequisite knowledge required: Text Section s 5. Calculate the coefficients for third-order polynomials in joint-space. Plot the joint angles, velocities, and accelerations. Assume the joint stops at intermediate points. This results in seven equations. The eighth equation can be generated by making assumptions such as a maximum allowable acceleration or an intermediate velocity.
For this problem we will assume that the joint will come to a stop at the intermediate point. Find the necessary blending time for a trajectory with linear segments and parabolic blends and plot the joint positions, velocities, and accelerations. The positions, velocities, and time duration for the three segments for one of the joints are given below. Determine the trajectory equations and plot the position, velocity, and acceleration curves for the joint.
The same can be found using the matrix equation of Equation 5. Find the joint variables for the robot if the path is divided into 10 sections.
Each link is 9 inches long. Find the angles of the three joints for each intermediate point and plot the results. Estimated student time to complete: 30 minutes, depending on programming expertise Prerequisite knowledge required: Text Section s 5. Show that the angle criterion is met. Can you determine from the root locus whether or not the system is stable?
Estimated student time to complete: 30 minutes Prerequisite knowledge required: Text Section s 6. Can you determine whether or not the system may become unstable as the gain changes? The roots are always on the left side, and therefore, the system is always stable. Estimated student time to complete: minutes Prerequisite knowledge required: Text Section s 6. Find a proper location for the zero and the loop gain. Angle deficiency: 3.
Find the location of an additional zero and proportional, derivative, and integral gains. Ignoring the inertia of a pair of reduction gears and viscous friction in the system, calculate the total inertia felt by the motor and the maximum angular acceleration it can develop if the gear ratio is a 5, b 50, c Compare the results.
Estimated student time to complete: minutes Prerequisite knowledge required: Text Section s 7. Each link is 22 cm long, made of hollow aluminum bars, each weighing 0. The center of mass of the second motor is 20 cm from the center of rotation. The worst case scenario for the elbow joint is when the arm is fully extended, as shown. Assume the inertias of the worm gears are negligible. Therefore, a new motor must be picked.
Two other motors are available, one with the inertia of 0. Which one would you use? Estimated student time to complete minutes Prerequisite knowledge required: Text Section s 7.
The smaller motor is better. Estimated student time to complete: 10 minutes Prerequisite knowledge required: Text Section s 7. Therefore 0. Pick 2 0. Therefore: 2 1 2 3 4 0. Estimated student time to complete: Variable depending on expertise. Prerequisite knowledge required: Text Section s 7. Solution: The accuracy with which this program will work depends on the processing speed of the microprocessor.
It also depends on the level of programming language and how efficiently it is written. We assume that the processor can accept and run a compiled C program, and that it is fast enough such that the execution of commands will not negatively affect the accuracy of the output timing.
Since only five distinct output voltages of 1, 2, 3, 4, and 5 volts are desired, we only need to generate 5 variations in the timing loops. We assume the output level will be indicated by an input port. Therefore, if input port 1 is high, the desired output level is 1 volts, etc. The following program is written in C language for execution by a Mini-Board microprocessor. It is the essentials of the program that are important here, not the actual program and the way it is written.
This program must be modified for use for any other specific microprocessor with its own unique programming syntax and requirements. In this program, the command motor 1,n indicates that the output port 1 is turned on at n 15 CC V. The command msleep m indicates a stop in execution for m milliseconds. Off 1 means output port 1 is turned off.
Since a sinusoidal out put is desired for a 5 volt input voltage, we need to generate a variable control timing for the pulse width modulation. We calculate the sine value for each degree between zero and 90 degrees. This allows for approximately 10 pulses per second. Since Mini-Board can generate voltages in both polarities, the program can generate a full sine wave. The program must be modified accordingly if the microprocessor cannot do this.
Be mindful of the problems associated with an H-bridges transistors turning on and off at inappropriate times. Estimated student time to complete: Prerequisite knowledge required: Text Section s Solution: The following program is written in C language for execution by a Mini-Board microprocessor.
It is assumed that an input to the microprocessor equal to 1 indicates rotation in the CCW direction, 2 indicates CW rotation, and a 0 means the motor should be braked. The total memory needed is 10 megabytes. For a bit per channel system, each pixel requires 2 bytes. The total memory needed is 20 megabytes. The assumption here is that the pixel count given is the total number for all three colors.
The actual memory is greatly influenced by the format in which the image is saved. A bitmap image needs much more memory than J PEG. Calculate the new values for the given pixels.
The remaining pixels on the perimeter will not be affected. Depending on how a new image is formatted, the pixels on the perimeter may be set to zero or the current values.
The new values for the image, assuming that the old file is copied into a new file, are: 4 7 1 8 3 3. Substitute 0 for negative grey levels. What conclusion can you make from the result? Solution: The mask will only affect the middle pixels.
The new values for the image, assuming that the old file is copied into a new file, are: 5 5 5 7 7 8 5 10 12 0 3 9 10 0 0 0 0 10 5 16 17 1 3 8 8 8 8 9 9 10 This can be an indication of an edge.
Estimated student time to complete: 5 minutes Prerequisite knowledge required: Text Section s 9. The new values for the image, assuming that the old file is copied into a new file, are: 5 5 5 7 7 8 5 10 12 0 3 9 10 20 13 13 6 10 5 16 17 1 3 8 8 8 8 9 9 10 When absolute values of negative pixels are shown, edges are no longer discernable. Which one is better? The new values for the image, assuming that the old file is copied into a new file, are: 5 5 5 7 7 8 5 0 0 0 0 9 10 20 13 13 6 10 5 0 0 0 0 8 8 8 8 9 9 10 This mask also shows the edge, but unlike the one in problem 9.
The new values for the image, assuming that the old file is copied into a new file, are: 5 5 5 7 7 8 5 5 8 0 2 9 10 0 0 0 0 10 5 8 12 0 0 8 8 8 8 9 9 10 At least for this image, the effect is similar to the mask in problem 9. The new values for the image, assuming that the old file is copied into a new file, are: 5 5 5 7 7 8 5 15 20 0 5 9 10 0 0 0 0 10 5 24 29 0 3 8 8 8 8 9 9 10 At least for this image, the effect is similar to Problem 9.
Estimated student time to complete: 10 minutes Prerequisite knowledge required: Text Section s 9. The median is 6. For 3c: 2,3,4,5,5,6,6,7,9. The median is 5. Find the value of pixel 3b when mask 1 is applied. Find the values of pixels 2b, 2c, 2d when mask 2 is applied. Find the value of pixel 3c when a 5 5 median filter is applied.
Find the area of the major object that results when a threshold of 4. Refer to the note on page for more information. Estimated student time to complete: Variable depending on the expertise Prerequisite knowledge required: Text Section s 9.
It is the essentials of the programming that are important here, not the syntax. You may use the proper syntax for the program you are using. This program may be written in countless other languages, both graphical and scientific.
In this program, the assumption is that the image input file is read from a data file or it is entered after initializing the array. Estimated student time to complete: Variable depending on expertise Prerequisite knowledge required: Text Section s 9.
You should write the routine such that the user can choose the size of the mask and the values of each mask cell individually. Using the Hough transform, determine which of these points form a line and find its slope and intercept. Estimated student time to complete: minutes Prerequisite knowledge required: Text Section s 9.
Solution: y x x,y m,c 0 2. Line 3 for point 5,4 does not intersect the remaining lines. The approximate slope and intercept of the line on which the other four points lay are 1. The routine should start at the 1,1 corner pixel, search for a nucleus, grow a region with a chosen index number, and after finishing that region, must continue searching for another nuclei until all object pixels have been checked.
Prerequisite knowledge required: Text Section s 9. The cells value is later checked until all are found and the cells are all zero. Each corresponding pixels value is changed from 1 to the region number. At the end of execution, the original image is changed to as many regions as necessary.
Since there will be no cells pixels left with a value of 1, execution ends. All segments will be 2 and larger in value. The program for growing a region based on 4 connectivity is very similar to that program, except that the search will follow the 4 sequence given in Equation 9. The remaining pixels are not connected to this region and will not be detected. As you notice, the image is different from the original. The program should ask you for moment indices.
The results may be reported to you in a new file, or may be stored in memory. Solution: The following program is written in C language. Thinness, based on 2 P Area. Center of gravity Moment 0,1 M about the origin pixel 1,1 and about the lowest pixel of a rectangular box around the key 2,2. The area may be calculated by 0,0 M , by region growing or by counting. The second moments about the centroids can be calculates as follows: 2 2 2,0 2,0 0,0 16 4.
The second moments about the centroids can be calculates as follows: 2 2 2,0 2,0 0,0 18 4. Estimated student time to complete Prerequisite knowledge required: Text Section s For example, different inputs and outputs may be selected, different fuzzy sets may be chosen, the ranges selected may be different, and alternate rules may be assigned.
Therefore, not only the solution is not unique, the result will also differ. This suggested solution may only be used as a guide. You may use this or any other available system. The inputs are how dirty the fabrics are and how much clothes are being washed, and the output is the wash time. The inputs may be the thickness of the steak and how cooked or rare it is desired to be. Estimated student time to complete: Prerequisite knowledge required: Text Section s The inputs are the speed of the car and the load on the engine, and the output is the gear ratio of the transmission.
The inputs are your effort level in the course and your exam grade, and the output is your letter grade. Estimated student time to complete: minutes Prerequisite knowledge required: Text Section s A. Open navigation menu. Close suggestions Search Search. User Settings. Skip carousel. Carousel Previous. Carousel Next. What is Scribd? Explore Ebooks.
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