# Help in Computing Inverse Kinematics of a 5 DOF Robot Config Its is a robot config with 5 DOF. We are provided 2 offsets d1 and d2. d1 and d2 are both 0.04 meter.

It is confusing for me alittle bit. I am attending lectures online but I am having trouble figuring out the angle joint configs and their mappings.

Is there a simulation software I can use to visualize and understand its parameters.

• Have you done the forward kinematics equations? If so, you should be able to enter values for $\theta1$ through $\theta5$ to determine the position and orientation of the final coordinate system {T}. Please let us know what you have done with that so we can help you determine the next steps for computing the inverse kinematics. – SteveO Oct 13 '18 at 3:38
• I have implemented the forward kinematics of the robot by deriving the transformation equations and then implementing this in code. I am able to correctly calculate the location and orientation coordinates of the end-effector tool-frame. I need to calculate the value of joint angles given the end-effector position coordinates. – Rishabh Agrawal Oct 13 '18 at 23:01
• Those $d_1$ and $d_2$ offsets make the inverse kinematics difficult. If $d_2$ was 0 we could partition the inverse solution into a wrist rotation and an arm position, but I cannot see a way to do that with a nonzero $d_2$. So look at your final T matrix and find similar terms, then trigonometrically manipulate these to reduce the items to a single variable. For example, the upper left term (end effector X mapped to global X) should not have a $theta_4$ component. And the Y and Z components of this vector may be able to be squared and added to eliminate $theta_4$. It’s challenging. – SteveO Oct 14 '18 at 14:16

Surprisingly, IK for a 5DOF robot arm is much harder than for a 6DOF arm. The reason is because a 5DOF arm cannot achieve an arbitrary pose in task space. Pose is typically expressed in terms of a 4x4 homogeneous transformation matrix ($$\in SO(3)$$) which encodes position (3 task-space DOF) and orientation (3 task-space DOF). To solve IK for your 5DOF robot you need to decide which task-space DOF you don't care about. For example you can compute IK that will take the end-effector to the desired position, and perhaps a desired roll and pitch angle, but you have no control over the yaw angle.

I tried to explain this at greater length with examples in a tutorial for the 4DOF case.

There is a beautiful man by the name of Chris Annin (beautiful as in what he did in the world of 6 axis robots). have a look at this video of his explaining inverse kinematics: https://www.youtube.com/watch?v=_rMUddhdk7o