Robot Arm Analysis: Linear Approximation | Massachusetts Institute of Technology

University
Massachusetts Institute of Technology
Course
Multivariable Calculus
Pages

1

Academic year

2022
Author

Sporkz
Views

61

p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:18px;font-family:ArialMT;color:#000000;} .ft02{font-size:18px;line-height:22px;font-family:ArialMT;color:#000000;} Robot Arm Complete Then, you can do a similar analysis for y. And to save time, we've put this on the p set. Youfind that delta y is approximately equal to delta theta. This is the linear approximation step. Now that we are solving the problem, let us check our work. It is known that delta L minusdelta theta equals delta x and that delta theta equals delta y. We want the value of delta xto be 0 and the value of delta y to be 0.1. One reason we want this is because we want thetip of the finger to move from 2 comma one to 2 comma 1.1. The change in x, or delta x, is 0. And the change in y, or delta y, is 0.1. We put that in herebecause delta L minus delta theta is 0 and delta theta is 0.1. We want to find the values ofdelta L and delta theta. We can read off directly that delta L is 0.1 and delta theta is also 0.1. We solve for delta L,which we get as 0.1, and then we solve for delta theta, which also comes out to 0.1.