X,y,z new coordinate calculation for joint rotations in CoppeliaSimEdu

[dis]

TL;DR Summary

I have problems with kinematic- > Rot(z,a1)Rot(z,a2)Trans(0,0,d) a1 and a2 angles d projection. My function was x = (d3+const)*math.cos(a1)*math.sin(a2) y = (d3*const)*math.const(a1)*math.sin(a2) but it not working.

I have created a 3D manipulator joint in CoppeliaSimEdu, I have the following joint rotation along the z axis, a second rotation joint raised in height and shifted along the x axis and further along the x axis is a directions joint. Or Rot(z,a1)Rot(z,a2)Trans(0,0,d) a1 and a2 angles d projection. But I have added a Dummy object to CoppeliaSim with which I set the x,y,z coordinates according to the kinematics calculations. But as far as I understand, I have a problem with the calculation of x and y coordinates, because the z coordinate is as it should be.

By connecting all the joints I got the matrix: [[cos(a1+a2), -sin(a1+a2),0,0],[sin(a2-a1),cos(a1+a2),0,0],[0,0,1,d ],[0,0,0,1]]

thus thinking that x = cos(a1+a2) + sin(a2-a1) y = -sin(a1+a2)+cos(a1+a2) z = d but the Dummy object doesn't move as it should, so I believe my x,y coordinates are wrong. How could I fix it?

 

[Filip Larsen]

I am not familiar with CoppeliaSimEdu, but for some interpretations of your initial description your 4x4 matrix seems correct except for $\sin(a2-a1)$ which should be $\sin(a1+a2)$. Note that two sequential rotations around any axis is equivalent to a single rotation about the exact same axis with the sum of the two angles.

I am not sure what you are saying next. Is (1, 1, 1) the position of your dummy object? And you expect it to shift around when you change your two angles and the offset? If so, it sounds like its more an issue with use of the program you use, so perhaps you can find an example that works and then try transform it to be applicable to your problem?

 

[dis]

Thanks. Found answer.
x = l1*math.cos(teta1)+l2*math.cos(teta1 + teta2)
y = l1*math.sin(teta1)+l2*math.sin(teta1+ teta2)

where l1 and l2 are constant