# how to solve inverse kinematic of 7-dof va1400 who has three offset configuration (shoulder elbow wrist)

va1400 kinematica model by Peter Corke MATLAB RVC-toolbox v9.10

clear
clc
deg2Pi = pi/180;

rz_mdh=[0,0,0,-90,0,90,0]*deg2Pi;
tz_mdh=[0,0,614,  0,640,  0,0]/1000;
tx_mdh=[0,150,0,  0,200,  0,30]/1000;
rx_mdh=[0,-pi/2,pi/2,-pi/2,-pi/2,pi/2,-pi/2];

L1_mdh= Link('d',tz_mdh(1),'a',tx_mdh(1),'alpha',rx_mdh(1),'offset',rz_mdh(1),'qlim', [-170 170]*deg2Pi, 'modified'  );
L2_mdh= Link('d',tz_mdh(2),'a',tx_mdh(2),'alpha',rx_mdh(2),'offset',rz_mdh(2),'qlim', [-70 148]*deg2Pi, 'modified' );
L3_mdh= Link('d',tz_mdh(3),'a',tx_mdh(3),'alpha',rx_mdh(3),'offset',rz_mdh(3),'qlim', [-90 90]*deg2Pi, 'modified' );
L4_mdh= Link('d',tz_mdh(4),'a',tx_mdh(4),'alpha',rx_mdh(4),'offset',rz_mdh(4),'qlim', [-150 175]*deg2Pi, 'modified' );
L5_mdh= Link('d',tz_mdh(5),'a',tx_mdh(5),'alpha',rx_mdh(5),'offset',rz_mdh(5),'qlim', [-150 150]*deg2Pi, 'modified' );
L6_mdh= Link('d',tz_mdh(6),'a',tx_mdh(6),'alpha',rx_mdh(6),'offset',rz_mdh(6),'qlim', [-45  180]*deg2Pi, 'modified' );
L7_mdh= Link('d',tz_mdh(7),'a',tx_mdh(7),'alpha',rx_mdh(7),'offset',rz_mdh(7),'qlim', [-200 200]*deg2Pi, 'modified' );
figure
botMotomanVA1407_mdh = SerialLink([L1_mdh L2_mdh  L3_mdh L4_mdh  L5_mdh L6_mdh L7_mdh]);
botMotomanVA1407_mdh.name='Motoman VA1400-mdh';
botMotomanVA1407_mdh.teach();


I have read paper Analytical_Inverse_Kinematics_and_Self-Motion_Application_for_7-DOF_Redundant_Manipulator and implemented all algorithm including inverse kinematic and Arm angle interval to avoid joints exceeding the limits. However it is invalid for non-spherical wrist configuration robot like Motoman VA1400.

Using Newton-like method with jacobian matrix is not better because of singularity.

This paper solves IK using Hessian Matrix ,but it does not elaborate the algorithm, it just provides the method to calculate Hessian Matrix.

Is there method to get the IK for VA1400 with specific Arm angle as the paper Analytical Inverse Kinematic Computation for 7-DOF Redundant Manipulators With Joint Limits and Its Application to Redundancy Resolution and paper Analytical Inverse Kinematics and Self-Motion Application for 7-DOF Redundant Manipulator mentioned