Self propelled lawnmower

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Executive Summary

In this report we will present our findings upon analysis and dissection of a Toro Self propelled Lawn Mower. Our report consists of Major Stake holders and Needs, Product use, Parts List, Assembly, Design for Manufacture and Assembly, Design for Environment, Failure Mode and Effects Analysis and Mechanical Analysis.

In the Lawn care industry, there are various stakeholders; Lawn owners, manufacturers, raw material suppliers, and direct customers. More detail as to the roles and needs of each stakeholder is elaborated in the Major Stakeholders and needs section.

In general, push mowers are relatively simple machines to operate. A simple pre-start check list is carried out, followed by a pull cord start up and holding down a throttle lever to sustain engine operation. There’s a gear shifter to engage and disengage the transmission into a 3 forward speeds and a neutral position where the mower is propelled by the user.

Upon dissection of the mower, we encountered a plethora of parts involved strictly in the drive train system of the mower. All parts involved with the transmission that were rebuild-able without causing complete destruction had been disassembled in dissection. The functions and manufacturing techniques involved in production of the parts themselves.

Our analysis also involved discovery of design for manufacture and assembly. The lawnmower had several visible signs of design choices made for ease of manufacture and assembly. Stamping of parts out of sheet metal is an effective process when producing a massive quantity of parts. Design for Assembly reduces overall costs of output by simplifying assembly and reducing turnout time. Other processes and their benefits are explored in the Design for manufacture and Assembly.

While analyzing the overall effect of the lawnmower in society with respect to the economy, energy consumption, greenhouse gas production, conventional air pollutants, and toxic releases, we came across astonishing numbers. It is difficult to compare the benefits of economic activity increase versus the effects of manufacture and transport in the sectors involved along the supply chain and manufacturing line of lawn and garden equipment.

In our search, we found it useful to perform Failure Modes and Effects Analysis (FMEA). In this analysis, we compare the products of failure severity, occurrence of failure, and ease of detection. For our purposes we performed the analysis from the perspective of the manufacturer. There were a couple of components in need of concern and analysis, namely the gas tank, the mower blade, and drive belt. Their defects are intensely explored in the FMEA section.

As part of durability of the lawnmower, we felt it was crucial and necessary to perform a mechanical analysis on a key component that connects user interface and the lawnmower’s operation. Through a series of finite element analysis with Solidworks and CosmosWorks, we were able to optimize stress distributions and cut down material costs.

Major Stakeholders and Needs

The self-propelled lawn mower has drastically improved the efficiency and quality of lawn mowing since the era of the push mower. The stakeholders involved include the customer, the manufacturer, the supplier of raw materials, and lawn owners. The customer can be anyone from a lawn owner to a commercial lawn mowing business. The customer must be ensured efficiency, quality, safety, and convenience. Therefore, it is essential that the self-propelled lawn mower is not too cumbersome, heavy, and well enough secured so that a customer of any size or strength can safely and effectively cut any lawn. This is also important when considering the lawn owner because the owner desires an attractive lawn, but wants to achieve this as quickly as possible so as to utilize the lawn. The customer also needs a lawn mower that meets the aforementioned requirements, but is durable and can be purchased at an affordable price. Once purchased, the lawn mower must be easy to clean and maintain and must incur minimal usage costs for the user to achieve great satisfaction with the product. The manufacturer's primary concern is minimizing the manufacturing costs so as to maximize profit. Since the manufacturer is responsible for producing a vast quantity of operative and safe lawn mowers, another of their needs is the efficient, reliable and inexpensive shipment of raw materials from the raw material supplier. The raw material supplier is concerned with properly executed marketing techniques so that the product is sold more, providing them with the opportunity to supply more materials. The raw material supplier and manufacturer’s needs can conflict with the customer needs in terms of cost of purchase because the customer desires a low purchase price, where the manufacturer and raw material supplier want a high selling price.

Product Use

The operation of this particular lawn mower is fairly simple, but it is very important to be aware of the safety concerns associated with each step. As long as a few precautions are taken you can easily ensure that the mower will not malfunction, and that the user will be safe throughout the entire operation.

The first step in using the mower is to check the gasoline and oil levels. When checking the gasoline it is important to do this in a well ventilated area, away from any ignition or sparking devices. If the engine requires gas it is important to refuel the engine after it has cooled off. If the engine is hot it is a good safety practice to let the mower cool for 10 minutes before adding unleaded gasoline. One final step that must be taken during refueling is ensuring the snug fit of cap on the the tank. This is important to maintain pressure on the engine and keep dangerous fumes from escaping.

The next step in operating the lawn mower is checking the oil level. You can easily do this by removing the dipstick on the side of the engine. You then must clean off the oil and dip it in to check its level. You then can tell by the markings on the dipstick whether or not adding or removing oil is necessary. This step is important to ensure that the mower is able to properly lubricate its engine.

Now that the oil and gasoline levels have been checked, you can move onto adjusting the cut height. For this step you need to evaluate the height of the grass you intend to cut. If the grass is more than 2 or 3 inches tall it is a good idea to pivot the arms into the higher slots like slot D, or E. If the grass is not very long the lower slots like A, and B will work well. Slot C would be a good choice for grass that is of a medium height. This step is very important because if the right height isn't selected you can either kill the grass (the setting was too low) or have the engine bog out (the setting was too high).

After the wheel height has been set, you can set the throttle control. If you are planning on starting the engine cold you need to move the lever on the throttle control to the 'choke' position. It will be important to move the lever off of the choke setting after then engine warms up. Also this level can control how fast the engine is going to run. You can slide the lever to up to the rabbit to open the carburetor fully or slide it back to the turtle to close the carburetor and slow the engine down. The fully open setting would be good when your cutting thick or long grass and the slower setting would be good for shorter grass.

The next step required to start the mower is to move the drive control bar to the position shown in the picture below. This must be done because of the safety feature built into the mower. This requires that pressure be placed on the drive bar in order to keep the engine running.

Now in order to start the mower the user must continue to hold the control bar in the position shown above. Now the user is ready to pull the pull start handle to turn the engine over. Sometimes multiple pulls will be required to get the engine started. If the engine doesn't start after 10 pulls the user needs to check all the previous steps to make sure they have prepared the engine properly for starting. Some additional things that can be checked if the engine doesn't start are the integrity of the spark plug, the condition of the fuel lines, the cleanliness of the air filter, and any obstructions or clogs in the carburetor.

Once the mower is started the user can push the drive control bar forward to engage the self propelled drive function. The way this works is when the drive arm is pressed forward it tightens up a cable which is attached to a bracket. This bracket is located on the back of the transmission. When this bracket has pressure on it it it rotates and brings the pulley in contact with the drive belt. In the picture below the drive control bar is half way pushed in, making it propel itself at about half its capable speed. When the bar is completely depressed the belt is in full contact and full speed is reached.

Part List

In order to complete our parts list we did a product dissection. Although we disassembled almost the entire mower there were some limitation. Since there are so many parts to the self propelled mower we decided to forgo removing the engine and all of its parts. We decided to make the drive train and its components the highlight of the product study. Some other limitations we faced was that in order to take certain parts completely apart, the part would have to be destroyed. This limitation was seen in the extremely tight fit of the tires on the wheels. Under close examination we determined that the rubber tires were cast with the wheel inside, and in order to remove it we would have had to cut the tires off to separate the wheel completely. We also discovered that the rear and front wheels were exactly the same except for the rear wheel gear riveted into the rear wheel. We figured this was to save cost on injecting the wheels. The wheels would be virtually identical until the rear wheel gear was later assembled (a process that the user could do by hand if he was replacing a wheel. This also allows the user to replace any of the wheels on the mower with one stock replacement part instead of two. An additional problem we faced was removing the rear differential (transmission). When we got to this part we also decided it would be best left intact. In the lawn mower users manual it tells you to have the transmission opened or serviced at a Toro certified service location. It warned that it would be very hard to reassemble the transmission and have it work safely if done on your own. We were able to find some exploded views of the gear sets within the differential housing in online parts catalogs. So because of the warning in the manual we decided that we would just study the outside of the housing and the parts drawings we found online.

Part # Name Weight Quantity Function Material Manufacturing Process Image
1 Front Wheel 1.8 lbs 2 Attaches to the front of the mower and allows the mower to roll horizontally Plastic Plastic Mold Injection
2 Rear Wheel 1.8 lbs 2 Drives the Lawnmower, translates drive shaft motion into horizontal movement (Exactly same as front wheel, only has a spot for the rear wheel drive gear to mount on it as shown in picture.) Plastic Plastic Mold Injection
3 Rear Wheel Drive Gear 2.1 oz 2 Translates the rotational motion of the drive shaft gear into rotational motion of the the wheel. Also the particular gearing provides more torque to the wheels. Steel Cast, Turning, milling
4 Drive Gear Shield 0.1 oz 2 Keeps grass and other particle from getting in to the drive gear mesh, also keeps the gears from leaving the gears. Black ABS Plastic Plastic Mold Injection
5 Shoulder Bolt Axle 1.2 oz 4 Attaches the wheel to the Pivoting arms which are then attached to the deck of the mower, allows the wheel to spin freely about the smooth section of the of the bolt. Steel Forged and rolled
6 Deck 15.4 lbs1 Houses the motor, and has separator areas where all of the different assemblies of the mower attach and connect into one. Also provides protection to the user from the spinning blade. Aluminum Cast

7 Front Pivot Arm 4.5 oz 2 Allows you to easily adjust the height that the front wheels will be at. Allows for cutting different lengths of grass. Steel and ABS Plastic Stamped steel with riveted peg. Plastic mold Injected, press fit together
8 Rear Pivot Arm 4.8 oz 2 Allows you to easily adjust the height that the rear wheels will be at. Allows for cutting different lengths of grass. Steel Cast, Milled, and Tapped
9 Front Pivot Arm Bolt 0.9 oz 2 Fastens the Front Pivot Arm to the lawn mower deck. It allows the poiot arm to rotate in this slot to e prvide different wheel heights. Steel Forged and Rolled
10 Tension Washer 0.05 oz 2 Provides an even surface for the Tension Spring to seat itself on. Steel Stamped
11 Drive Train Gear 0.8 oz 2 Uses the rocking key to engage the drive shaft and there for provide power to the wheels. It has slots on the inside radius where the rocking key turns and grabs hold of the gear. Steel Forged, and turned
12 Tension Spring 0.025 oz 2 Keeps the drive train gear tight against the rear wheel gear. This spring rests and maintains tension between the E-Clip, washer and the drive gear Steel Wound
13 Clutch Washer 0.025 oz 2 This part attaches to the drive shaft and engages the rocking key into the drive train gear. This piece has a V-shaped recess that presses against the rocking key arm and engages it. Nylon Cut, and Spun
14 Rocking Key 0.1 oz 2 Rocks in the drive shaft and drive shaft gear to lock the key in places so the gears begin to turn. Then when the mower is pulled in reverse it rocks the other way and disengages the gears. Steel Forged
15 E-Clip 0.02 oz 2 Locks the tension spring and drive train gear on the rear axle. Steel Stamped
16 Shoulder Nut 0.1 oz 4 Allows you to fasten the shoulder bolt to the pivoting arm that attaches to the deck. Steel Forged and tapped threads
17 Pivot Arm Nut 0.1 oz 4 Allows you to keep the pivoting arm fastened to the deck Steel Forged and tapped threads
18 Drive Train Cover Bolts 0.3 oz 2 Secures the drive train cover to the deck, over top of the drive train gears. Steel Forged and rolled
19 Pulley Tightening Bracket/ Belt slip Guard 3.2 oz 1 Provides link between the rotating transmission and the drive control cable. When the cable is tightened it pulls this bracket back, which in turn engages the drive train pulley belt. In addition this bracket sits on either side of the belt near the pulley and keeps it from falling off the pulley when the belt becomes loose. Also when the pulley is in a slip condition it provides a spot for the slack in the belt to build up. Steel Stamped, drilled, and then bent
20 Rear Differential Transmission 8.5 lbs 2 Houses the gears that translates the power of one belt spinning from engine into two drive outputs on either side of the housing. This part converts linear motion from the belt into rotation of the 2 drive shafts. Steel Stamped and drilled
21 V-belt 6.5 oz 1 This part links the drive shaft from the engine to the pulley on the rear drive differential. This part just sits loose when the drive is not engaged and then is tightened when the cable is pulled tight to engage the drive components. Rubber Extruded, and bound
22 Blade 2.3 lbs 1 This rotating object with sharp edges that cuts the grass. Steel Forged, drilled, and then ground sharp
23 V-belt pulley 2.5 oz 1 This part is located on the top of the rear differental and links the v-belt to the gears in the rear differential. Steel Cast, turned, and milled.
24 Throttle/Drive Control Cable Housing 0.4 oz 1 This housing protects the drive cable from rusting or breaking. Plastic Extruded
25 Throttle Drive Control Cable 0.3 oz 1 This part connects the pulley tightening bracket and the control bar on the handle. It tights the pulley and engages the self propel function when you push forward on the control hand. Steel Braided
26 Handle Hand Nut 0.15 oz 2 This part allows you to tighten the connection between the upper and lower portions of the handle without any tools. You can simply turn these with your hand. Black ABS Plastic Plastic mold Injected
27 Handle Pivot Bolt0.3 oz 2 Allows you to pivot the two parts of the handle about this point. Lets the upper part of the handle fold forward over the front of the mower to save space. Steel Forged and Rolled
28 Transmission and Pulley Gear Cover 5.6 oz 1 Covers the transmission and drive components. Protects the pulley and belt from getting debris in them. Plastic Plastic Mold Injected


The following diagrams from the Toro website show how all of the dissected parts fit together. The part numbers for each part are labeled on the assembly drawing.

Assembly 1

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Assembly 2

Assembly 3

Assembly 4

Design for Manufacture and Assembly (DFMA)

Design for Manufacture consists of reducing costs of a product in the manufacturing stage through the proper selection of manufacturing methods. It is important, however, that the quality of the product is not reduced when attempting to reduce cost at this stage of the product life cycle. When examining and dissecting our product, we observed that several of the parts were stamped from sheet metal or plastic injection molded. Several pieces such as the drive gear shield, handle hand nut, and plastic knobs on the pivot arms can all be plastic injection molded at once, just as the tension washer and e-clip can be stamped from sheet metal at the same time. Another cheap and efficient manufacturing method is press-fitting. A few of the parts on the lawn mower are press fitted, which saves money compared to the use of some adhesive. This also drastically minimizes the time needed to manufacture the product. These are cheap yet effective methods of manufacture, representing a well executed design for manufacture. Another example is the manufacture of the deck, which is cast from aluminum. These are cheap yet effective methods of manufacture, representing a well executed design for manufacture. The material choice of aluminum is also an excellent demonstration of design for manufacture. The deck is responsible for protecting the user from the spinning blades so the material must be strong, yet lightweight so as not to fatigue the user. Therefore, aluminum is a great choice because even though it is high-priced, it is light and durable. Casting a part is more costly than stamping one, but the shape of the deck is too complicated to allow for stamping. Other parts such as the v-belt pulley and throttle drive control cable can be made from less expensive materials like steel because they require endurance, but not to be lightweight. Although it is rather heavy, steel does not fatigue that easily, which is essential to parts that are subjected to large amounts of stress.

Design for Assembly is meant to reduce the complexity of the product assembly and in doing so, minimize the ultimate cost of the product. In the product dissection, we found all of the parts to be easily removed signifying that the lawn mower was also easy to assemble, exhibiting a properly executed design for assembly. We can observe from the shape of the deck that the bolts and screws attaching the wheels, pivot arms (height adjustment mechanisms), and drive gear shield are able to be grasped effortlessly. In the case of the pivot arms, there is a recession for the nut to fit that holds the wheel onto the mower, which is very convenient. The transmission and gear cover was also easy to be removed permitting v-belt, pulley, or transmission inspection/cleaning. As we dissected the lawn mower further, components like the transmission became more difficult to disassemble, but an everyday user doesn't normally need to access such parts. Pieces such as the v-belt that might need to be replaced due to failure were very easy to remove and replace. The handle pivot bolts were made with a rounded head, which is shaped as such to allow rotation of the upper part of the handle. Another demonstration of a superior DFA includes the similitude of the parts like the pivot arms, pivot arm nuts, and the shoulder bolt axles. The corresponding location of these parts allows for them to be made identical, regardless of whether they are in different places. It would be very inefficient and costly to make different parts when they could be made the same. This simplicity of assembly reduces the time required to build the product, allowing for mass production at a minimal cost.

Design of Environment

In our Design for Environment analysis we used the EIOLCA program through EIOLCA is Environment input output life cycle analysis. With this program we can analyze how investing a certain amount of money in one sector will affect the rest of the economy. In analyzing the outputs for our sector, Lawn and garden manufacturing, economic activity is encouraged in most sectors, employment rises in the central states, namely Tennessee, Arkansas and Wisconsin. Our biggest concerns are in greenhouse gas production, and energy consumption, and toxic releases. Power supply tends to be a main producer of gaseous pollution and energy pollution. In the manufacturing process, sites, or factories, produce a massive amount of stationary pollution that is approximately four times greater than the pollution caused by mobile sources involved in the manufacturing process. Throughout the life-cycle of the lawn mower, every use produces air pollutants, and every 2 months the Lawnmower engines use up a small percentage of oil. The life expectancy of the Lawn mowers lasts 3-5 years. In the end of the mower's life, much of the components, minus the plastics are recyclable. Engines and frame can be melted down and reformed for other products.

Sector #333112: Lawn and garden equipment manufacturing

Economic Activity: $1 Million Dollars

Displaying: Economic Activity


Sector #333112: Lawn and garden equipment manufacturing

Economic Activity: $1 Million Dollars

Displaying: Conventional Air Pollutants


Sector #333112: Lawn and garden equipment manufacturing

Economic Activity: $1 Million Dollars

Displaying: Greenhouse Gases


Sector #333112: Lawn and garden equipment manufacturing

Economic Activity: $1 Million Dollars

Displaying: Energy


Sector #333112: Lawn and garden equipment manufacturing

Economic Activity: $1 Million Dollars

Displaying: Toxins Released


Carnegie Mellon University Green Design Institute. (2008) Economic Input-Output Life Cycle Assessment (EIO-LCA) model [Internet], Available from: <> [Accessed 23 Sep, 2008]


FMEA (Failure mode and effects analysis) is used to determine the potential problems with designs. It takes each component in a mechanical system and analyzes its failure modes and effects using three main criteria. These criteria are severity of the failure (S), probability of occurrence of the failure (O), and ease of detection of the failure (D). Each of these is ranked on a scale of 1 to 10. For severity, 1 is least severe and 10 is dangerous or catastrophic failure. For probability of occurrence, 1 is very unlikely and 10 is almost certain. For ease of detection, 1 is easiest to detect and 10 is impossible to detect. Once each component is assigned one number for each of the three criteria, the numbers are multiplied together to determine the RPN (risk priority number). This number can range from 1 to 1000. The higher the RPN for a specific component the greater the chance that this component needs to be looked at and improved. Along with assigning a numerical value to the risk of certain components, FMEA also attempts to determine the origin of the problem and possible solutions to improve components. It is important to note that design controls and recommended actions are intended to help the manufacturer improve the problem. The following table provides an FMEA analysis for the key components of the lawnmower.

Item Function Failure Mode Effects of Failure S Causes of Failure O Design Controls D RPN Recommended Actions Responsibility and Deadline Actions Taken S O D RPN
Wheels Translate power from drive shaft to horizontal motion Plastic dries out and cracks Mower can get stuck and won't move 8 Use of mower in dry weather too often 5 Use plastic that is less likely to dry out 2 80 Fatigue testing Wheel manufacturer 8 5 2 80
Wheels Translate power from drive shaft to horizontal motion Plastic dries out and cracks Mower can get stuck and won't move 8 Use of mower in dry weather too often 5 Use plastic that is less likely to dry out 2 80 Fatigue testing Wheel manufacturer 8 5 2 80
Blade Cut grass Dulls Grass cutting in ineffective 8 Natural wear with time 7 Use harder material that is less likely to dull 2 112 Fatigue testing Design engineers 8 7 2 112
Blade Cut grass Rusts Grass cutting is uneven 8 Natural wear with time 7 Use material that does not rust 3 168 Waterproof coating Design engineers 8 7 3 168
Belt Transfer power from engine to transmission Rubber dries out and breaks Rear wheel drive won't work 6 Use of mower in dry weather too often 5 Provide extra belts with mower 5 150 Analyze tension in belt Design engineers 6 5 5 150
Tires Provide traction on wheels Tread wears with time Mower will lose traction and ability to climb hills 4 Natural wear with time 7 Consider different tread pattern that takes longer to wear 1 28 None, unlikely occurrence 4 7 1 28
Rear Wheel Gears Gears down power from engine to rear wheels for increased torque Teeth break Rear wheels will not turn evenly or consistently 1 Too much strain on rear wheels 2 Consider different material for gears 9 18 None, unlikely occurrence 1 2 9 18
Cables Attach to mounting bracket to engage transmission Stretch It will be difficult for the user to engage drive mechanism 4 Overuse of drive system 5 Improve connection points 7 140 Failure tests of connection points Design engineers 4 5 7 140
Cables Attach to mounting bracket to engage transmission Break User cannot engage drive mechanism 1 Overuse of drive system 2 Lower required tension in cable by adding a system that provides mechanical advantage 1 2 None, unlikely occurrence Design engineers 1 2 1 2
Gas Tank Holds fuel for engine Leak Engine will not be able to operate 6 Puncture from debris 4 Locate critical puncture points and reinforce them 6 144 Puncture testing Design engineers 6 4 6 144
Wheel Brackets Allows user to change ride height and attaches wheels to chassis Knobs for changing height break Height cannot be changed 8 Constant Pressure on weld seam 7 Replace with removable piece so that it can be easily replaced if it does break 1 56 Knob redesign Design engineers 8 7 1 56
Wheel Brackets Allows user to change ride height and attaches wheels to chassis Constant bending can cause plastic deformation Bracket is at risk of breaking 7 User bends bracket too much when changing height 4 Use material with a higher elastic modulus 1 28 None, unlikely occurrence 7 4 1 28
Driveshafts Transfer power from transmission to rear wheels Shear Rear wheel drive won't work 1 Engaging rear drive while rear wheels are stuck 1 Reanalyze the key points where the driveshaft is attached 2 2 None, unlikely occurrence 1 1 2 2

From the FMEA we can determine the most high risk means of failure of the lawnmower. These failures have an RPN of over 100 and include stretching of the cables, leaking of the gas tank, and the blade getting rusty or dull. Although none of these failures are catastrophic they are all significant and can lead to the lawnmower not working optimally. All of these failures are due to regular wear and tear that occur from using the mower.

Mechanical Analysis

For the mechanical analysis we decided to examine a key bracket on the transmission casing. This bracket (Pulley Tightening Bracket, part number 17 on the parts list) is mounted to the top of the transmission casing by two quarter inch bolts. When the user pulls the lever to engage the drive mechanism a cable tightens and pulls on this bracket. This forces the entire transmission to rotate upwards about the axis of the driveshaft, engaging the transmission via a pulley that is connected to the engine. The purpose of this exercise is to estimate the amount of force required by the user to keep the drive system engaged. This will involve a static analysis of the pulley tightening bracket. Once the tension in the cable is determined, we can employ FEA to locate the maximum stresses in the bracket and possibly optimize it.

The above figure is a side view of the pulley tightening bracket. ‘T’ is the tension in the cable; ‘W’ is the weight of the transmission; ‘O’ is the axis of the driveshaft; ‘D1’ is the distance from the point on the bracket where the tension is applied to the axis of the driveshaft; ‘D2’ is the distance from the bolt holes on the bracket (where the weight of the transmission is focused) to the axis of the driveshaft; ‘α’ is the angle between the direction the tension is applied and D1; ‘β’ is the angle between the direction that the weight of the transmission is acting and D2. Since the system is in static equilibrium we can sum moments about point ‘O’ and set it equal to zero (taking counter-clockwise to be positive). For the purpose of this analysis it should be noted that the reaction forces that oppose the weight and tension act about the driveshaft at point 'O'. The reaction forces do not affect the analysis as they act through the point where moments are summed and therefore are not included in the diagram.

∑ Mo = 0 = TD1sinα – WD2sinβ

Solving for T,

T = WD2sinβ/D1sinα

Plugging in all known values we are able to closely estimate that the tension in the cable, ‘T’, is equal to 13 pounds.

The following image is a Solidworks model of the pulley tightening bracket.

The following image is a stress plot of the bracket that was made using COSMOSWorks with a tension force of 13 pounds applied to the connection point of the bracket and the cable. The part is constrained at the bolt holes and the weight is acting on the bottom face of the bracket. This plot shows that the maximum stress in the bracket is 6,540 psi and the yield stress of the steel is 89,980 psi. This gives a factor of safety of 13.76 which is well within the acceptable range and will be the basis for maintaining during optimization.

As it is now, the bracket has a weight of 0.23 pounds and a volume of 0.83 cubic inches. Optimization was done to remove excess material in areas of low stress concentrations. The following image shows a stress plot of the bracket after the optimization.

After optimization, the bracket has a mass of 0.20 pounds and a volume of 0.70 cubic inches. The new value for the maximum stress is 7,148 psi. This maintains a factor of safety of 12.59 which is still within the acceptable range. With this new design, each unit will save 0.03 pounds of material. It is assumed that this bracket is stamped. The excess material could be recycled and when the part is produced on a large scale this may have a significant effect on material costs. It then becomes an issue of whether or not it will be cost effective to change the dies in the stamping machine to cut out the new pattern.

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