Hello,
So, I have 2 trigonometric equations, the unknowns here are q2 and q3.
The 2 equations are:
Py=2*cos(q1) * ( cos(q2+q3) + 3*cos(q2) )
Pz=2*sin(q2+q3) + 6*sin(q2) + 14
First I tried on paper to get some function q3=f(q2), and that's what I ended up with:
q3=atan((Pz/2-7-3*sin(q2))/(Py/2/cos(q1)-3*cos(q2)))
Then I tried to solve only the first equation, substituting q3 with that function of q2 like this:
solve((Pz/2-7)==(sin(q2+q3)+3*sin(q2)), q2);
And the answer was: "Warning: Possibly spurious solutions."
I've also tried this, as I've seen in some post here
eqns = [(2*cos(q1)*(cos(q2+q3)+3*cos(q2))) == Py, (2*sin(q2+q3)+3*sin(q2)) == 0];
Unsuccesfully tho
In another attempt I wanted to do in Matlab the same thing I did on paper, that is to get some q3=f(q2) and substitute it afterwards in the equation, but I ended up with complex numbers, and that's not something I wanted because q2 and q3 are angles for my robot, and Py and Pz are coordinates of the robot, so I can't get complex angles.
eqn = sin(b+c)+3*sin(b) == z/2-7;
In this case b=q2, c=q3 and z=Pz. I tried it for the second equation and I got complex numbers too.
In my last attempt I tried a more direct approach
Result=solve(2*cos(q1)*(cos(q2+q3)+3*cos(q2)) == Py,...
2*sin(q2+q3)+6*sin(q2)+14 == Pz ,q2,q3)
But I ended up with complex numbers again and a very long solution too. By no means the result that you should get from a robot with that has the first rotation about the Z-axis and the last 2 about the Y-axis.
