I am working on a robot with multiple joints but just in 3DOF. I have resolved parameters of the first and second dof however in the third dof, there are 8 links. I have the base and target points of the links in this DOF, and I have been able to parameterize some arbitrary Cartesian coordinates for these links. The main objective is how to calculate the angles of joints holding these links.
For example, below are the coordinates for a given target point (8.6005, 0.4073, 5.3550), if the base of links in the 3rd DOF is (3.9228, 1.7883, 2.0000).
V0 = [3.9228, 1.7883, 2.0000]
V1 = [9.2359, 5.9971, 2.4194]
V2 = [4.9271, 10.7107, 2.8388]
V3 = [8.2702, 16.1519, 3.2581]
V4 = [12.1939, 21.1906, 3.6775]
V5 = [16.4524, 16.4285, 4.0619]
V6 = [20.7109, 11.6664, 4.4462]
V7 = [24.9693, 6.9042, 4.8306]
V8 = [8.6005, 0.4073, 5.3550]
How can I compute thetas 1-8?
Note: the values of the three axes (X, Y, Z) in above V1-8 kept changing!