E91: DYNAMICS

Lab 4: Design, Analysis, and Prototyping of an Elliptical Machine

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Introduction

The goal of this lab is to customize an elliptical machine to a team member’s physical dimensions. This lab should get you better acquainted with SolidWords and prototyping techniques. Additionally, you will have the opportunity to design a simple mechanical system with a four bar linkage.

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Background

An elliptical trainer (also cross trainer) is a stationary exercise machine used to simulate walking or running without causing excessive pressure to the joints, hence decreasing the risk of impact injuries. It is comparable to a treadmill in its exertion of leg muscles and the heart. However, because the user’s limbs remain in continuous contact with the machine, its operation limits the dynamic loading of bones and joints to generally harmless levels. This non-impact aspect appeals to those with recent injuries, chronic knee problems, and the obese, who cannot tolerate a treadmill[1].

The elliptical machine can be thought of as a crank-rocker four-bar linkage designed to guide your foot to travel in a path that closely resembles an ellipse as you exercise. Unfortunately this path can not be adjusted. Tall persons like Prof. Cheever, and vertically challenged persons like Prof. Hsieh are forced to exercise their legs following the same exact leg motion. Even though Prof. Cheever’s natural leg strides are larger than Prof. Hsieh’s, they are forced to execute the same foot path when they exercise an the elliptical machine. This path may feel natural for most people of average size, but may feel awkward for Prof. Cheever and Prof. Hsieh. Prof. Cheever is forced to 1

take smaller strides than he is used to and Prof. Hsieh has to take bigger strides than she usually takes when she walks. Obviously the design of the elliptical machine is compromised. In this lab you will customize an elliptical machine to a team member’s dimensions in which the path of the elliptical machine will match as close as possible the actual stride of his/her legs during walking. Additionally you will design two sets of linkages that will match the path of the team member’s feet (one linkage/foot) when he/she exercises on the elliptical machine during an actual walking motion

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Lab

Think of yourselves as the engineering team of a company whose primary business is to customize exercise and/or physical training equipment for the rich and famous. You have just received an order from a celebrity whose physical dimensions just happen to exactly match those of your chosen team member. You must now lay out an analysis and design plan to come up with a prototype machine. In the first part of the lab, devise a plan for achieving the goals of the project. Break down the goals and objectives into a list of tasks and sub-tasks. Determine which of the tasks must be executed sequentially and which of the tasks can be executed in parallel with other tasks. Your list should, at a minimum, include the following tasks in no specific order: • Create a schematic of an elliptical machine with the crank, coupler, follower, and frame clearly denoted. • Measure the angles and link lengths of an actual elliptical machine and analyze the motion of the machine using the four–bar linkage program provided in matlab.zip. • Determine which of your team member will be your mock client. • Have your “client” try out a conventional elliptical machine and get input from your “client”. • Design your four–bar linkages. • Manufacture a prototype. Next, you must figure out how to divide/sub-divide the list of tasks among your team members. Determine how many people will be required for each task and devise sub-teams in charge of completing the various tasks. You may want to assign each person to multiple sub-teams depending on the number of tasks you come up with. Execute your plan. In the process, you may find you will need to make adjustments and changes to your initial plan such as changes to the task list, sub-team compositions, task assignments, etc. Note the changes and adjustments you make to the original plan. Four–bar Linkage Program The main file in matlab.zip is fourbar analysis.m. When you run this program, it will ask you whether you would like to input your data using a file (*.dat) or by typing it in via the command line. Four sample input files are included in matlab.zip. The file fourbario.dat contains the input variables for a generic four–bar linkage. The file doublerocker.dat contains the input variables for a double rocker mechanism and draglink.dat contains the input variables for a drag link mechanism. The fourbar analysis.m program will compute all the joint angles and the angular velocities for a four–bar mechanism in operation. These are then stored in an output text file named filename.txt. In your analysis, you can edit fourbario.dat to reflect the values you obtained in your measurements.

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Figure 1: A stick figure of legs in three extreme positions during stride. Getting Input from the Client As part of the process, you should have your client try out a conventional elliptical machine, make sure you note how far his/her legs must move. Measure the angles his/her joints make using a geniometer. (You may want to look up what a geniometer is and figure out how you can devise one for this part of the lab since one may not be available to you.) Note how much the rest of your client’s body move. Are there any parts of this machine that are particularly badly designed? Well designed? Why is each structural part of the machine there? What are uncomfortable configurations for your client? You should also figure out a way of plotting the path of your client’s heel over time during a natural walking stride. Designing the Linkages Read the Synthesis notes from Dr. Vijay Kumar made available on the course website. Figure 3 shows a stick figure of legs in three extreme positions during stride: minimum (blue), neutral (green) and maximum (red). The minimum position is defined as the position of the leg when the joint angles are smallest. In the neutral position the joint angles of the hip and knee are 0 degrees and in the maximum position the joint angles are greatest. Angles are measured in the local frame, i.e. relative to other limbs. For three position synthesis (see synthesis.pdf) you will need to pick three different positions of your client’s foot. For example you could take the three positions of the heel as shown in Figure 1. The bar that the user will be standing on will be called the platform. See Figure 2. The platform will give you the three positions of the coupler from which you will determine the four–bar linkage for your customized elliptical machine. The position of the ankle gives you three positions of a point on the platform, but not the angle of the platform relative to the ground (or heel). You will need to determine the three angles that will allow you to create a feasible elliptical machine. Designed your four–bar linkage, analyze and plot this linkage by using fourbar analysis.m, compare the output motion of the platform with the plotted path of your client’s heel. Iterate between your design process to get your four–bar linkage to follow actual path of the foot as close as possible. Plot both the motion of the foot from the four–bar linkage and the actual data on one graph. Prototyping Prototyping is an important part of the design process. It allows you to quickly check your design for feasibility, functionality, manufacturability, and other factors for very cheaply. Additionally, it gives you a physical intuition of the kinematics of the device. In addition to physical intuition, semi-functional mockups are often used to explain concepts to people, in this case your client(s), or if the company is starting out, to venture capitalists if you’re pitching the concept. In these cases, besides getting the kinematics right, there are several other important aspects of the prototype such as • Aesthetics: The device should look appealing.

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Figure 2: Plot of leg with platform attached to the foot in three different positions. • Robustness: Having the device fall apart during a demonstration is disastrous. • Features: There should be a reason for the existence of every component on the device. Using your analysis and design, you will now build a functional mockup of a new and improved elliptical training device, specifically tailored to your client’s dimensions. It must, at a minimum, • allow constrained motion of the legs in some optimal pattern (you choose what optimal means), • be able to fit in a 11” x 35” x 35” box, and • be able to show the intended motions for a miniaturized person using it (e.g. a working four bar linkage). Based on your observations of current elliptical machines (or other exercise machines you may have seen), you may wish to add functionality to your device. In Class Pitch Select two of your team members to present your device in a 2 minute presentation to the class as if you are selling the concept to potential investors. You should highlight the features that make your device unique, useful and desirable. The in class pitch will constitute 10% of your grade. Extra Credit Most exercise machines can be adjusted to a persons dimensions by adjusting prismatic or revolute joints to change the height or angle of the seat for example. The elliptical machine however does not offer such a feature (as far as we know). Can you add a joint in which the path of the elliptical could be tuned to fit a person’s natural strides? If so, incorporate it into your prototype. Are there any elliptical machines out there with such a feature. Are there any patents on such a design?

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Figure 3: Photograph of an elliptical machine prototype. Note that the main frame serves as a main stand and the body of the person is rigidly attached to this stand.

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Report

For this lab you will have to write a group lab report and an individual lab report. The group lab report should include the following: 1. Goal: The goal of the project (1-2 sentences); 2. Project Plan: The list of tasks that you came up with initially, assignment of the tasks to each sub-team and the composition of each sub-team. A timeline showing the planned execution of your plan, i.e. the order that tasks were suppose to be executed (you can have parallel execution of tasks if you deemed that to be feasible, efficient, etc.). A timeline showing the actual execution of your plan including early completions and delays of tasks. A description of how things went, whether you had to make any changes to your initial plan. What worked well, what did not work well, what was easier than you had originally thought, what was much harder than you had originally thought? (1 page maximum of text, you can use additional pages for tables, schematics, flow charts, etc.) 3. Analysis: The analysis of the conventional elliptical machine. Include any equations, diagrams, schematics, and all the plots generated by fourbar analysis.m. (1 page maximum of text, you can use additional pages for figures, schematics, etc.) 4. Client Input: The analysis of your “client’s” needs. Include a brief description of your client’s assessment of his/her experience with a conventional elliptical machine. Describe how you collected all the necessary measurements, e.g. joint angles, limb lengths, path of your client’s heel during a normal walking stride, etc. Include a description and schematic of any measurement devices you designed/made/invented, i.e. a goniometer. (1 page maximum of text, you can use additional pages for figures, schematics, etc.) 5. Design: Include the plot where you plotted the both the motion of the foot from the four–bar linkage and the actual data you collected, the linkage design, the angles of the three positions from the measured leg data. Discuss how you chose the platform angles. (1 page maximum of text, you can use additional pages for figures, schematics, etc.)

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6. Prototyping: Include pictures of your creation, the important properties chosen, a description of the features of your design and the rationale for each. Describe what you have chosen for your optimality metric. Include print outs of CAD files used to cut the pieces and the scale (ratio) of the model versus reality. The individual lab report should include the following: 1. A list of your responsibilities. 2. A list of your team members’ responsibilities broken down by team member. 3. A list of tasks you completed either individually or with other team members. 4. A list of tasks each of your team members completed whether by themselves or with other members. 5. A short description of what you thought your role in the team was. Your indivdual lab reports should be no more than 2 pages long.

References [1] Wikipedia. en.wikipedia.org/wiki/Elliptical_trainer

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