Is My Lego-Based Scale Design Accurate and Feasible?

[Physics_wiz]

So, we have to build this scale in mechatronics class that weighs things as small as a dime to as large as however we want, but it has to weigh a dime. I came up with this idea that will be constructed with legos:

A pully (20 cm radius) will be fixed on a shaft with a cup kindda thing hanging on one end to put the weight in (I'll put another one on the other side to balance it). On the other end of the shaft, a small gear (1 cm radius) will be fixed and connected to a rack. The spring will be be on top of the rack so that when the rack moves, it pushes on the spring.

I chose to use a pully with a large radius and a small gear to multiply the force on the spring since a dime doesn't weigh that much at all and the smallest spring I found had a spring constant of .17 N/mm. Here's my work:
The weight pulling down on the pully will create a torque on the shaft = Fr
T = (.01 N) (.2 m) = .002 Nm. *.01 N is approximately the weight of a dime*
The gear then is subjected to the same torque and has a radius of .01 m, so following the same equation T = (F2) (r)
.002 Nm = (F2) (.01 m)
F2 = .2 N
F2 is the force from the small gear on the rack, which is the same as the force on the spring. So, by using a big pully and a small gear I multiply the force of a dime by 20. An optical encoder will be fixed on the shaft to see how much the shaft turns and calculate the weight of the dime.

Are my calculations right? Do you think the friction of legos will make this project a failure? Think oil or grease will help with the friction that much?

Here's a picture if you can't visualize it: www.geocities.com/iamjico/spring.bmp

 

[FredGarvin]

Your reasoning is sound. I think the details may bite you in the end though. The way I see it, your biggest issue to overcome is the leggos being stiff enough. Chances are the leggos will absorb a lot of the force and that force will go into deflecting the teeth, or simply deflecting the supports for the shaft and gears. Do your best to make sure that the design is as rigid as you can possibly make it.

Friction, as you mentioned, will also be a factor at the low weights, but that should be easier to overcome than the stiffness.

 

[Cliff_J]

Playing devils advacate, why not just apply KISS and construct a support structure to dangle a spring and then a cup attached to the spring. Attach a linear encoder and you can still measure the movement and you have no friction to worry about.

In your diagram, depending on the materials, the weight of the string on the left side may be more than the dime! Meaning you'd need to balance out the scale to equilibrium by having a heavier cup and so on.

Mimicing a balance beam scale may work too, a linear encoder on the far side of the beam with a spring there would be another approach with only the pivot to add friction. Or you could use a substantial beam difference to get a high mechanical ratio to make the scale sensitive enough for the small weight of the dime and have the other end pull a rope to a rack and pinion. And testing such options should make for a good report as well.

just a thought...

 

[Physics_wiz]

I actually went to the lab and built it today and it worked a lot better than I thought. I don't have an encoder on the shaft or even the pully yet, but I found a small 3 mm radius gears that multiplies the force on the rack a lot more than with 1 cm radius gears. I might be able to get away with a 6 cm radius pully (CD) after I found that small 3 mm gear.
As FredGarvin said, the legos were not that rigid but I'll make them a lot more rigid. They're already rigid enough to measure within a small % error, but it's not that hard to make them more rigid. The friction is a lot less than I thought it would be...I might not even need to put any oil, because the friction will be so small that calibration will take care of it.
There are some problems with the ideas Cliff_J posted. First, if I go with the KISS idea, I'll have to use one spring to measure a dime and a tennis ball (my goal is to be able to weigh anything from a dime to a tennis ball). The spring will go back and forth when the object is put on it and the optical sensor will keep on recording encoder pulses and give me a false weight. I don't know if this will happen with my design or not but it should be less than just putting an object on a spring. Also, a substantial length lever won't work because the scale has to fit in one cubic foot. With the gear and pully configuration, I can multiply the force by any number I want depending on the size of the pully up to like 50x (15 cm radius pully with the 3 mm radius gear).