# Homework Help: Robot w/ 2 links

1. Oct 25, 2007

### engineer23

1. The problem statement, all variables and given/known data

I have a device with two links (see attached diagram). The device uses the joint angles to determine the position of the end effector (x,y).

a) Potentiometers are 2% accurate. Find the maximum endpoint error for the device.

b) If you use optical encoders, how many bits are needed to make the endpoint error less than 2 mm?

2. Relevant equations

Based on the diagram,
I have x = .5 cos (theta1) - .5 cos (theta1 + theta 2) and
y = .5 sin (theta1) - .5 sin(theta1+theta2)

Is my trig right?

2% pot. means that accuracy is +/- 7.2 degrees (since 2% of 360 is 7.2)

3. The attempt at a solution
For part a, do I just choose two arbitrary angles, add and find the difference between the actual x,y position and the x,y position at max error? (ex. choose 30 and 120 as joint angles, calculate position, then recalculate with 37.2 and 127.2, and find difference between position values)

I am a little confused on b. I want resolution to be 2 mm. How do I find max/min (x,y) position? Range/resolution = 2^n....solve for n?