Process¶

A spring load test experiment is to be set up. The required materials for this setup were: a weighing scale, weights, springs, hooks, measuring scale. The following materials were used to carry out this experiment in place of traditionally available materials. Paper clips were used as hooks, bolts with known weights were used as weights, and the rubber bands were the springs whose spring constant was to be measured.
Measure the weight of several bolts at the same time. Divide total weight by number of bolts to get the average weight of one bolt. In our case, one bolt weight approximately 10 grams.
A paper clip was duct taped to the edge of table and one end of the rubber band was attached to it. A ruler was also duct taped along the side of the paper clip to act as a measuring scale.
A face mask was used as a bag to hold the screws. The stretching string of the face mask was cut off and a non-stretchable shoe string was used in its place. This was to ensure that there was only one spring in the system, ie. the rubber band.
The weights selected were in intervals of 20g starting with 0g to 100g.
The initial length of each rubber band was measured and recorded. Then 20g of weight was added into the mask and the mask was attached to the bottom end of the rubber band using another paper clip. The displacement was recorded.
Weight was gradually increased till 100g and length of rubber band was recorded.

The recorded data was used in excel to form a scatterplot. A line of best fit was generated using Excel's trendline function which utilises the least square optimization model.

Below are the images of the setup and different graphs formed.

Figure shows the setup used to measure the spring constant of the rubberband before the stretchable mask strings were removed¶

Figure shows the setup used to measure the spring constant of the rubberband using a shoe string to prevent unnecessary complications in the spring system ie. introducing a second spring.¶

The bolts were weighed and each bolt weighs about 10g.¶

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The weights were added in the mask itself. Each bolt weighed about 10g. Weights were increased at an interval of 20g. In this picture, the weight is about 40g.¶

Measurements were taken at each intervals and recorded in a tabular form against the weight. The ruler attached on the side was used to measure the displacement. Extension (in metres) was calculated using the data.¶

The image does not do justice to the ruler scale but it was infact intact. The ruler was just a little worn out.¶

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Excel was used to create a graph of Weight (N) vs the Extension (m). Line of best fit was created using excel's trendline function. It utilises the least square optimzation model.¶

The following images are for each type of rubber band and their data obtained and recorded in tabular form¶

The following are the graphs obtained for each of the datasets above respectively. The slopes represent the k values for each of the rubberbands.¶

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Discussions¶

What could you have done better in your experiment design and setup?

A better measuring scale could have been used. A piece of paper could have been attached to the bottom edge of the rubber band which would point precisely to the reading on the ruler. This would improve accuracy of the readings.

Multiple trials with the same rubber bands could have been done to obtain an average reading for each weight.

A better way to hold the bolts such as a plastic bag could have been used. Something with a more negligible mass would provide more accurate readings.

Discuss your rationale for the model you selected. Describe any assumptions or simplificaitons this model makes. Include external references used in selecting or understanding your model.

The rationale for this model is the fact that for a large part of their stretching, rubber bands act similar to springs. They obey Hooke's law and as such, similar experiment such as that for spring constant can be used for the rubber bands.

The assumptions in this experiment are as follows:

The weight of the mask + shoestring is assumed negligible when in fact it does have a slight mass that affects something as elastic as rubberbands.
The weights of the bolts are assumed to be acting at a single point downwards.
It is assumed the rubberbands act linearly obeying hooke's law. With the limited weights that have been used, the rubberbands still obey hooke's law within the specified range. However, given the elasticity of rubberbands, they would quickly deform at higher weights. Only the linear range of the rubberbands have been considered.

External references used to set up this experiment is: Stretching Rubber Bands [1]

Justify the method you selected (least squares, nonlinear least squares, scipy.optimize.minimize(), Evolutionary algorithm, etc. ) for fitting experimental data to the model, as well as the specific algorithm used.

Least square method was utilised using Excel's trendline function. It provides the best error estimate using a line of best fit from the scatter plot obtained by the data. The model selected was supposed to behave linearly within the given range of operation. The slope of the line of best fit provides the k value (as per Hooke's law experiment) which has been calculated for all 4 of the rubberbands.

How well does your data fit the model you selected? Provide a numerical value as well as a qualitative analysis, using your figure to explain.

The gentle hold rubberband 2 and the small rubberband are the closest fits according to the expected linear model. They also have similar k values. While the gentle hold rubberband 1 also has the same k value, it has a greater deviation from the line of best fit. For the quantitative values, refer to the equations on each graph. They provide the estimate using the line of best ft for that particular rubberband. All of the rubberbands more or less have a perfect linear relationship. However, this is still because of the assumption number 3 as stated above. If weights are increased, the linear relationship will not be maintained.

What are the limits of your model, within which you are confident of a good fit? Do you expect your system to operate outside of those limits?

The rubberbands function within the limits of the scope of the project. The primary function of the rubberbands is to keep the gripper in a closed position, which should be the grippers natural state. The servo motor is going to be pushing against the rubber band in order to open the gripper and hence the system should operate within the weight limits in this experiment.

Goal¶