I had no experience at all with Matlab. Please forgive me if I make any horrible or stupid mistakes.
I am not asking for whole solutions, just trying to find the right way to solve problems in MatLAb.
Problem in details is below:
Basiclly , I am trying to write a function in Matlab which takes 3 inputs x , y , z which indicate the position where I want to arm to reach or point at.
f_1, f_2, f_3 are the angles as shown in the picture.
L is constant, L = 10
I have the following two equations:
sqrt(x^2 + y^2) = L * cos(f_2) + L * cos(f_2 - f_3) ·········································(1)
z = L * sin(f_2) + L * sin(f_2 - f_3) ····························································(2)
After square the (1) on both side and add to the (2), I can get
x^2 + y^2 + z^2 = 2L^2 + 2L^2 * cos(f_3)·····················································(3)
since x,y,z,L are known, I can easily get cos(f_3), with acos(), i can get f_3.
But when I am substitute the f_3 back into the equations into (1) and (2) to get the f_2.
I found the equation becomes really complicated.
for example, look at equation (2)
z = L * sin(f_2) + L * sin(f_2 - f_3)
after expanding. I got：
z = L * sin(f_2) + L * ( sin(f_2) * cos(f_3) - cos(f_2) * sin(f_3) )·····················（4）
then I substitute cos(f_3) and sin(f_3) into the equation （4）， I got:
z = L * sin(f_2) + (x^2 + y^2 + z^2 + 2L^2) * sin(f_2) / 2L - L * cos(f_2) * sin(f_3)
which is way too complicated to finish, since I still need to substitute cos(f_2) with sqrt(1 - sin^2(f_2) ).
I am really sorry for the long paragraph of explanation, I just want to make myself clear.
I just wonder if there are any function in Matlab which are meant to solve problems like this?
Or what is the better way to solve f_2 for this problem?
