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Shiyas Basheer Enda Brady Sean McKay Brian Speller 12/12/2011 Dublin Institute of Technology Child Pedal Cart Design Design Project

Child Pedal Cart Design

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Page 1: Child Pedal Cart Design

Shiyas BasheerEnda BradySean McKayBrian Speller12/12/2011

Child Pedal Cart Design

Design Project

Page 2: Child Pedal Cart Design

Table of Contents

Design Brief.................................................................................................................................................2

Key aspects of the design........................................................................................................................2

Constraints..................................................................................................................................................2

Assumptions................................................................................................................................................3

Calculations.................................................................................................................................................4

Steering Calculation:................................................................................................................................5

Torsion in the Steering Column and the axle:..........................................................................................6

Gear ratio and the resulting speed calculation........................................................................................7

Minimum area of key in the rear axle:...................................................................................................11

Bearings.................................................................................................................................................11

Conclusion.................................................................................................................................................13

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Page 3: Child Pedal Cart Design

Introduction

Design Brief

We were asked to design a pedal cart for a child between the ages of 4 and 10 years

old. The cart must be suitable for a 5th percentile 4 year old to the 95th percentile 10

year old.

This means that the 5% smallest 4 year old can operate the cart and a 95% biggest

10 year old can also operate the cart also.

Key aspects of the design

For this report certain key areas of the cart were focused on as they were deemed to

be the most important aspects of the pedal cart. These aspects were:

• Computer models of the components that make up the cart and an assembly of

these parts.

• Analyzing the forces and failure modes of the rear axle and specifying an

appropriate diameter for the axle.

• Calculating a suitable gear ratio for the cart.

• Specifying a suitable bearing for the wheels.

• Calculating the forces in the various steering members of the cart and specifying

appropriate diameters for the members.

Constraints

Before it is possible to start to design the cart or preform any calculations there were

a number of design constraints that would have to be considered. These constraints

were to insure that the child would be safe when operating the cart and also that they

could operate the cart comfortably. These constraints were that the child would be

able to comfortably reach both the pedals and the steering wheel. This would mean

that the seat would have to be adjustable as a 4 year old and a 10 year old must be

able reach the controls. It was decided that when the seat is in the fully forward

position the distance between the back of the seat to the pedal at its furthest position

from the seat should be the fully extended leg length of a 5th percentile 4 year old. It

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Page 4: Child Pedal Cart Design

was also decided that the distance from the seat to the steering wheel in this seat

position should be the total grip length for a 5th percentile 4 year old. This means

that when the 4 year old is sitting properly in the seat they can reach the pedals and

the steering wheel comfortably.

It was then decided that when the seat

was in the fully back position the 95th

percentile 10 year olds leg will not

have to bend at an angle of less than

60° angle at the knee. This would

mean that the distance between the

back of the seat and the pedal when it

is in the position closest to the seat

has to allow the leg to only bend to

60º. It was also necessary that the 10 year old would be able to reach the steering

from this seat position. If these criteria are met then a 95th percentile 10 year old will

also be able to pedal and steer comfortably.

The next constraint is the speed that the

child will be able to pedal the cart at. It is

important that the child can pedal the cart

at a speed that is fun but still safe. It is

necessary to choose a gear ratio that will

allow a child to move the cart off from a

standing start easily but not allow then to

travel at a dangerous speed.

As well as reach the steering wheel it is also important that the child can apply

enough torque to turn the wheel and overcome the friction between the tires and the

road. This will be calculated from the maximum torque a 5th percentile 4 year old

can exert.

Assumptions

We also made some assumptions such as the coefficient of friction between the tire

and the asphalt to be 0.7 which was reasonable, two-third of the weight acts on the

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Page 5: Child Pedal Cart Design

rear wheels of the cart for a 10 year old child, half of the weight acts on the rear

wheel for a 4 year old child, that the human force is proportional to weight. We also

assumed that the maximum revolution per minute a child can pedal is 40 – 50 rpm

and the anthropometric data to be same for boys and girls. Talking about

anthropometric data, it is the measurement of the size and proportions of the human

body, as well as the parameters such as reach and visual range capabilities.

Accurate data on height, weight, limb and body segment sizes were needed to

design the various parts in our cart. Anthropometric data enabled us to properly size

items, including system interface to fit the user. We selected our design to be for 5 th

percentile 4 year old and 95th percentile 10 year old. This means that for selected

anthropometric measure, such as height, the lower limit of our range is the height of

a 5th percentile 4 year old boy and the upper limit is the height of a 95 th percentile

10year old boy.

We found the following anthropometric data for a 4year old – total leg length

(445mm), total arm length (415mm), total grip length (340mm), shin length (275mm)

and total height (975mm) and for a 10year old- total leg length (810mm), total grip

length (580mm), shin length (484mm) and total height (1490mm).

We also assumed that the child foot force to be half of the foot force of an adult as

we couldn’t find any data on the force exerted by a child.

Calculations

There were six different calculations which were carried out on the pedal cart and the

design of many of the components depended on the results of these calculations.

Calculations were carried out to aid in the design of the steering mechanism and to

ensure that a 5th percentile 4 year old could easily turn the wheels. Calculations were

also carried out on the steering column to ensure that it was of adequate diameter so

that a 95th percentile ten year old could not cause failure due to torsion. Similarly, a

calculation was carried out on the rear axle so that it was of adequate diameter so

that it would not fail due to torsion. A calculation was also carried on to determine the

necessary gear ratio so that both a 5th percentile 4 year old and a 95th percentile 10

year old can both pedal the kart easily and at reasonable but safe speed. A

calculation also had to be carried out on the key which went into the rear axle to

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Page 6: Child Pedal Cart Design

ensure that it was of adequate area so that it wouldn’t fail due to shear. Finally, a

calculation was carried out to determine the quality of bearing required so that it

would not fail due to wear until after at least 10,000 hours of usage. In reality, there

were many more calculations which could have been carried out but due to the

limited scope of this design project, it was decided that those six were sufficient.

Steering Calculation:

The mechanism used for the steering consisted of a steering wheel connected to a

steering column which has a hook at the end of the column. This hook is connected

to a tie bar which rotates the wheels based on how much the steering wheel is

turned. As the pedal kart had to be suitable for both a 5 th percentile 4 year old and a

95th percentile 10 year old, the steering mechanism on the kart had to be designed

so that even a 5th percentile four year old could rotate the steering wheel and turn the

front wheels.

The friction force on the front wheels times the mean diameter of the hook creates a

torque in the steering column which a 5th percentile 4 year old has to overcome. It

was previously assumed that a 5th percentile 4 year old can exert 5.37Nm of torque,

that the total weight of the 5th percentile 4 year old and kart is 24kg, the coefficient of

friction is 0.7 and that half the weight acts on the front wheels. Inputting these values

into the torque equation:

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Page 7: Child Pedal Cart Design

This implies that radius of the hook must be less than 0.065 metres or 6.5

centimetres for a 5th percentile 4 year old to turn the wheels.

Torsion in the Steering Column and the axle:

The steering column had to be of adequate diameter so that a 95th percentile 10 year

old could not cause failure due to torsion. The equation used is the torsion equation:

Where:

T is the torque (Nmm)

R is the radius of the shaft (mm)

τ is the maximum shear stress(N/mm2)

J is the polar moment of inertia for a round shaft which is equal to π d4

32mm4

Using the previous assumptions that the maximum torque a 95th percentile 10 year

old can exert is 16,010Nmm, that the shear strength of 080M40 steel is 370N/mm2

and a safety factor of 5:

16,010

π d 4

32

=74d2

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Page 8: Child Pedal Cart Design

Solving for d, gives a diameter of 10.35mm. This was rounded up to 12mm in our

actual steering column.

The next calculation which was carried out was to ensure that the rear axle was of

adequate diameter so that it wouldn’t fail due to torsion. This calculation actually

shows how interlinked many of the calculations were as the torque in the rear shaft

was calculated to be 29,047Nmm in the calculation on the necessary gear ratio.

Again using 080M40 steel with shear strength of 370 N/mm2 and using a safety

factor of 5:

29,047

π d4

32

=74d2

Solving for d gives a diameter of 12.6mm. This rounded up to 16mm in the actual

rear axle.

Gear ratio and the resulting speed calculation

A calculation was carried out to determine the necessary gear ratio so that both a 5 th

percentile 4 year old and a 95th percentile 10 year old can both pedal the kart easily

and at a reasonable but safe speed. Again, using previous assumptions for these

calculations:

The foot force a 5th percentile 4 year old can exert is 259N.

The foot force a 95th percentile 10 year old can exert is 776N.

The radius of the rear wheels is 11.75cm.

The radius of pedals is 8cm.

The total weight force of a 5th percentile 4 year old is 235.44N.

The total weight force of a 95th percentile 10 year old is 529.74N.

1/2 the weight of a 4 year old acts on the rear wheels.

2/3rd's the weight of a 10 year old act on the rear wheels.

The coefficient of friction between the wheels and concrete is 0.7.

The max RPM is 55 for a 5th percentile 4 year old and 65 for a 95th percentile

10 year old.

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Page 9: Child Pedal Cart Design

As can be seen in the picture above, the child inputs a torque into the front sprocket

which is equal to the child’s foot force times the moment arm of the force which is

assumed to be equal to the radius of the pedals. This torque is different for the 5 th

percentile 4 year old and the 95th percentile ten year old as they can each exert a

different foot force.

The torque in the rear axle is due to the friction force on the rear wheels times the

radius of the wheels. Again this is different for both the 5 th percentile 4 year old and

the 95th percentile 10 year old as the friction force acting on the rear wheels depends

on the child’s weight.

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Page 10: Child Pedal Cart Design

Using these values, the gear ration for both the 5th percentile 4 year old and 95th

percentile 10 year old was calculated using the following equation.

This implied that the front sprocket on the pedal kart had to be 2.14 times the

diameter of the rear sprocket. This also implied that the angular velocity would be

2.14 times greater at the rear sprocket than at the front. Using the assumptions for

the RPM in the front sprocket for both a 5th percentile 4 year old and a 95th percentile

10 year old and converting this to radians per second:

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Page 11: Child Pedal Cart Design

The linear velocity of the kart was then worked out using the following relationship,

where r is the radius of the wheel and ω is the angular velocity in the rear sprocket:

The maximum velocity of a 5th percentile 4 year old is 1.45m/s while the maximum

velocity of a 95th percentile 10 year old is 1.71 m/s. These are reasonable but safe

speeds and where judged to be acceptable for the pedal kart. A tabulated form of the

calculations for the gear ratio from excel can be seen below:

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Page 12: Child Pedal Cart Design

Minimum area of key in the rear axle:

The rear axle was connected to a rear wheel by a key; this key had to be of sufficient

area so that it would not fail due to shear. The maximum force in the key is equal to

the maximum torque in the rear axle divided by the radius of the shaft.

The key was made out of 080M40 medium carbon steel which has shear strength of

370 N/mm2 and using a safety factor of 5.

The actual area used for the key was much larger than 50mm2 as this is a very small

area.

Bearings

A calculation was carried out to determine the quality of bearing required so that it

would not fail due to wear until after at least 10,000 hours of usage. The bearing will

be connected to a shaft on one of the wheels and the shaft will be connected to rear

axle.

Ball bearings are generally standard items and can be purchased from specialist

manufacturers. For a given bearing the load carrying capacity is given in terms of the

basic dynamic load rating and the basic static load rating. The basic dynamic load

rating, C is the constant radial load, which a bearing can endure for 1*106

revolutions. The life of a ball bearing, L, is the number of revolutions (or hours at

some constant Speed), which the bearing runs before the development of fatigue in

any of the bearing components. Our task was to determine the catalogue rating

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which can then be used to find the appropriate bearing from a manufactures

published ratings for our specified rotational speed.

Assuming pitch circle radius to be 24mm and using the torque from the previous

calculations, first we found the tangential force (Ft) acting on the axle using:

Then we found the separation force (Fs) using Pythagoras theorem:

Now total force was calculated:

Force P on the bearings was found to be:

Using the below equation Catalogue rating was found:

Where:

Ccat=Catalogue radial rating

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PF

2606.738N

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Ld= required design life (revolutions or hours)

nd= required design speed (rpm)

Lcat=catalogue rated life (revolutions or hours)

ncat= catalogue rated speed (rpm)

k=3 for ball bearings

According to the chart below the found rating was way smaller that the fact is that we

could use any bearings.

Conclusion

In doing this project we discovered that when using a safety factor of 5 that the rear

axle will need to be made from 12.6mm diameter solid steel bar, The steering bar

needs to be made from 10.35mm solid steel bar and the key way areas on the rear

axle for the drive wheel and the sprocket need to have an area of 30.19mm. It was

also calculated that the wheel bearings will need to be MM201K bearings as they

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Page 15: Child Pedal Cart Design

have an appropriate life span at the loading the kart will put on them. the hook on the

end of the steering bar also needs to have a diameter of 65mm to give the child

enough leverage to turn the steering wheel.

We also discovered that when the seat is in the fully forward position the distance

from the seat to the pedal needed to be 445mm as this is the leg length for a 5th

percentile 4 year old. The seat will also be able to be adjusted 100mm back from the

fully forward position to accommodate a 95th percentile 10 year old. We got these

values from the anthropomorphic data available in the library. We also used the

anthropomorphic data to work out the positioning of the steering wheel.

We decided early on in the project that the kart was unlikely that the frame of the kart

would fail. If we were doing this project again we would include force calculations for

each member in the frame so we could insure that it would be strong enough.

In doing this project we were faced with a number of challenges. The first of these

was that the anthropomorphic data for children was not that widely available for

children. As a result of this we used half the value of the adult data for a number of

our calculations. This means that some of our calculations for steering forces and

pedaling forces are not accurate.

Overall this project was challenging but when the tasks were broken down and

distributer between the team members we were easily able to do them. The main

problem that we faced was the lack of available resources for required data.

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