# Thread: Inverse Kinematics of a Open-loop chain (SCARA robot arm) Abacus Join Date
Sep 2020
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## Inverse Kinematics of a Open-loop chain (SCARA robot arm)

Hello,
This is my first post, and I need to know how to solve the IK problem for a kinematic chain with 3 rotating links/joints;

(JOINT)--------(JOINT)---------(JOINT)--------[END EFFECTOR]

And if there is a good visualization and schematization tool that I can use.
It's for a class project.  Reply With Quote

2. ## Re: Inverse Kinematics of a Open-loop chain (SCARA robot arm)

The question is how many degrees of freedom each joint has, and how many degrees of freedom you want to solve for the end effector.
If you have only three degrees of freedom total, and only need position, not orientation, for the end effector, then the problem has zero, one, or two solutions, corresponding to a quadratic equation.
You typically configure the first point to point the rest of the effectors at the end effector in a plane (using atan2 to solve for the angle) and then use "two-bone IK" for the other two joints to attempt to reach the position projected to that plane (this is where the quadratic equation comes in.)  Reply With Quote

3. mcardoso Relay Join Date
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## Re: Inverse Kinematics of a Open-loop chain (SCARA robot arm)

The world of kinematics is a deeper rabbit hole than you might realize at first. Forward kinematics (I know the joint angles, where is the end of my robot?) for a robot are relatively straightforward to compute and can be handled as a trig problem. Inverse kinematics (I know where I want the end of the robot, what joint angles do I need to get me there?) is much more difficult.

For simple robots, such as a SCARA, you may be successful approaching the inverse kinematics problem from a purely geometric approach. Solve the trig problems for the forward kinematics and then rearrange the equations to solve for joint angles rather than XY coordinates.

The more rigorous approach which scales well to 5 and 6 axis robots is to use the homogenous transformation matrix to describe how each link in the robot transforms the coordinate system of the linke before it. You can stack these matrices to solve a serial linkage like a robot arm.
https://modernrobotics.northwestern....tion-matrices/

The subject is deep but fascinating. I recommend the book Introduction to Robotics: Mechanics and Control by John J. Craig
https://www.amazon.com/Introduction-.../dp/0201543613
It is the single best resource I've found for actually learning this stuff.

-Mike  Reply With Quote