Conventionally, the inverse and forward kinematic solutions of parallel robots are hard to come up with due to multiple constraints and complicated geometric structures. Moreover, both the analytical or geometric solutions seemed to be useful ONLY in certain cases.
In order to solve this hard problem in a more simple way. I saw the original problem from the reverse side and came up with an efficient and general method called Backward-Floating-Base-Jacobian Method(BFBJ). Any type of robotic structure, including parallel arm(Stelwart platform, delta robot, dual arm) or serial arm(Stanford arm, industrial robotic arm, kuka arm) even the humanoid robot and quadruped robot, can be solved by this SIMPLE method.
This idea is simple but powerful and general.
Render Animation for 6 degrees of freedom of Delta Arm.
Traditionally, the delta arm has only 3 d.o.f. The moving base can only move in x,y,z direction and cannot rotates at any angle in the space, which largely reduced the mobility for industrial manufacturing. However, extra degrees of freedom provided by three extra motors on the top of the disk makes the entire system too complicated to find the analytical solutions.
By using the Floating base backward Jacobian, adding three or more degrees of freedom to the original system will be easy to be solved. So our new Delta robot can provide 6 d.o.f including the position and orientation of the base. And this type of arm can also be used as a CNC machine.