I was asked by a professor for the model of the arm. He described it below.
The models are the mathematical representation, they are used to position the servos and the gripper. These models could be a system of differential equation, a matrix representation of the coordinates of the gripper in terms of the coordinate of the base of the arm, and maybe others.
It is important for you to realize that we will use the arm to teach math. We don’t need to solve any specific problem, we need to create a problem that in order to be solved the robotic arm has to follow a path described by a model which contains the math we need to teach in a specific course.
Do any of you have a clue as to what he is asking for?
I think he is asking for an equation to solve a Kinematics problem for a robot arm. If the axis are located inline (0 deg, like the tibia and femur servos) or in an angle of 90 degrees (femur and coxa servo) this can easly be solved my geometry. This is what we use in the hexapods, and what I used in the robot arm.
If the arm has the joints in a different angle (like Jonny did with the coxa joint on his stalker design) http://i531.photobucket.com/albums/dd355/innerbreed/100_1170-1.jpg
He need another solution involving matrix calculations. Every matrix in this equation represents a transformation/rotation between 2 coordinate frames. Mind that these are pretty complex and take away a lot of processor power. That’s why we don’t use them. For forward kinematics there is a Denavit-Hartenberg solution that can do the trick. I’ve got it somewhere in my notes for a hexapod leg. If there is need for an IK solution of this kind I would point him at chapter 6 of the book “Theory of Applied Robotics, Kinematics, Dynamics, and Control” by Reza N. Jazar. This chapter explains how to solve an IK problem for an 6DOF robotic arm.
Hope this helps
Xan
Edit: Note that there is no “one size fits all” solution when it comes to kinematics. As for the hexapods; It is easy to change size or start angles. But the formula is designed for horizontal movement(coxa) connected to vertical movement(femur) connected to vertical movement(tibia). It the servos are put in a different order or in another angle the formula needs to be redesigned. So as for the robot arm, they need to put a equation together that fits the hardware.
He is relating this to the D arm, which I believe is referred to as a 3DOF planar arm (meaning 3 DOF on the same plane), with base rotate and wrist rotate. The guy asking has a masters and a phd in the maths. I gave him the spreadsheets showing the formulas and he told me he didn’t understand them. Thanks for the input. Ill provide him with your advice. Thanks!
The robot arms from LM all have the same design when it comes to math. (with one exception) The only thing that varies is the length of the links between the joints. This is in the configuration file.
The exception I talk about it the wrist rotation kit. This adds an extra joint. We have not included this joint in the IK solution because it makes it hard to control with a remote. Tried it
Here are some different robot designs:
Typical R|-R_|_R design. Equal to yours
Cylindrical configuration R||P_|_P
Stanford robot arm R|-R_|_P
There are many more mechanical setups you can think of. The arms you sell have a spherical movement. Not all jobs require that. For example pick and place robot’s that assemble PCB’s need a large X and Y movement and a really small Z movement. Those robot’s use a different setup.
Xan, Thanks for the reply. No offense but I already knew most of that.
Zenta, Yeah I dunno why a professor is asking me for a math model for the arm. But I try to give the customer an answer.
I guess there is a big difference between defining the problem on paper, and solving the problem for a certain microcontroller, and therein lies the confusion. Thanks again!
Thanks for the input. Ill provide him with your advice. Thanks!
