User:MAE412 D

                                        MAE 412: Final Project

                                     Design for SHRIMP front Leg

                                             Shawn Moran
                                             Mike Pienta
                                             Justin Ross
                                            Shajan Thomas

Introduction:

The problem we were faced with was to design a 4 bar that allowed the wheel travel from point A to point B without going through the given obstacles. All the dimensions are given in the figure to the right. The ground joins have to be located within the box shown. For this project we had three different designs we had to come up with. The first was to design the 4bar to have the shortest total link length. The second was to design the 4 bar to reduce the maximum input torque required on the input link. The final problem was to reduce the fluctuation of torque in the input link.

Idea Generation:

As a group we came up with a few different ideas that didn’t really work. We tried to imagine a 4bar that would work for getting the wheel from A to B but could not come up with one. We eventually created a MATLAB program that would go through all the possible combinations and come up with the best 4bar. This program was created to find the shortest 4bar. The programs for the last two problems were not created but in the MATLAB program it calculated the torque and forces on all of the bars. The MATLAB code we used was submitted online through UBLearns.

Description of mechanism:

When we designed the 4bar we tried to get it to go through the points A and B. In the picture u can see a print screen from an automation of the 4bar. As you can see the 4bar is shown by the multi color links while the points A and B as well as the vehicle box and the step are shown by the black lines.

Dynamic Designer:

The model we used in the dynamic designer is shown below. This model was done using numbers that we recieved from out MATLAB code and then changed a little bit to make it fit better.

Shown below is the output velocity and acceleration using the Dynamic Designer for the 4bar shown above.

Simulation Based Design:

Used a method for synthesis as described in the text using the assumption that theta 3 is equal to theta c, the coupler angle. This leaves 6 free variable chooses, which are used to determine theta 2, theta 3, theta 4, in the A and B positions. This allows us to determine the magnitudes of all the links. Once this is determined checks are used to make sure that the links are attached to the chassis and that the link lengths are of appropriate length (not zero). Next a check is ran to make sure that the system meets grasshoff criteria and is either a double crank or a crank rocker, with r2 being the crank. The system is tested for collision. If any of these tests fail, one of the angles are changed and the system is run through again. If the system passes all of these checks, its length is compared to the length of the previous best solution and the best solution is kept.

This is where the problem starts. To get an answer that is specific to within a degree we would need to have 2.1 quadrillion iterations. If we started running this code would not finish until the beginning of next semester (I expect). A while loop was developed. The while loop focused on convergence of a correct answer. It would change one variable until the desired result, for example, minimum length was as small as possible. Then it went on to the next variable. This failed. After over specifying a single variable the other variables could not be varied without creating an increase in length, since the first variable was set in respect to the other angles. So the algorithm was changed to try and resolve this factor. It was redesigned so that each variable was changed a small amount. The program then checked for a positive or negative change and adjusted the angles again. This worked well. However, if the initial guess was not correct the program could never converge, in other words back to square one.

Going back to the four loop an educated guess for a range of answers for each variable was made, and the iteration step size was reduced to find some reasonable answer. This process failed an abundance of times, since an answer was rarely returned (most were rejected for reasons such as not being attached to the chasse, or links that were zero in length). However, solution were found, and these solutions were optimized in the while loop code.

Finding the torque on the fourbar system meant finding the velocity and acceleration at each position. This was accomplished by differentiating the loop closure equation.

Analysis:

Because all of our 4bar formulation was done using MATLAB and was automated the calculations were all done internally. Our MATLAB programs had breaks in their checks so there are solutions that we got that don’t fit the criteria. Some of these solutions are shown below.

Below you can see the flowchart we used to program the MATLAB code.