Inverse Kinematics: Oscillators and Multi-Bar Links

[Trying2Learn]

TL;DR Summary

Is it practical?

Good Morning

May I first ensconce this question in a related issue?

-----------------Related Issue-----------------------

Consider a 1D harmonic oscillator (mass, stiffness damping). The analysis of this structure bring many issues to light, regarding vibrations (no damping, under-damping, critical, over-damping, number of solutions, complex analysis, modal analysis, etc.).

Real world mechanical devices, however, are much more complicated.

Still, we study the fundamental oscillator because it provides a foundation -- a language of terms, concepts -- that are fundamental to machine vibrations.

One might say that the "distance" between the fundamental issue (and is simple issues) and the real-world applications, is relatively, short.

With that as the foundation, I turn to the issue for myself: inverse kinematics.

---------------Question at hand-----------------------

In forward kinematics (for open links), the issue is: given the angles of each link, where is the distal tip?

In inverse kinematics, the issue is: if we want the tip to be at a certain point, what are the angles of each link from the other?

For a simple 2 bar link, we learn the complexity of this issue. However, once we rise above three links, or add in constraints or obstructions, the topic is extremely complicated. In fact, one might say that the "distance" between the issues raised in a simple 2-bar link, is very far from real-world applications; so far, in fact, that the study of 2-bar inverse kinematics is rendered relatively useless.

In fact, it seems that in real-world applications, in 3D, with obstructions, one approaches the solution path more by trial and error than any analysis.

If you disagree, do not get angry: just explain. For that is what I hope to understand -- why I am wrong.

 

[Baluncore]

In fact, it seems that in real-world applications, in 3D, with obstructions, one approaches the solution path more by trial and error than any analysis.

I believe the thing you must avoid is a mathematical approach. You need to get closer to reality, so you can see where the problems lie, and what is really happening.

The trial and error employed is all in the mind and on paper. No hardware is built during the design phase. Start out alone, then bring in an accomplice.

1. Come up with a potential solution in your head, that looks like it might work, then sketch the mechanism. Machine design is an art, initially black, it only becomes a science with experience.

2. Repeat the thought process and sketching, until you are convinced it could work. You might now understand the problem.

3. Then put numbers on the dimensions that constrain operation. Compute the length of the links, and the position of the hinge pins, using simple geometry and arithmetic. If the numbers don't add up, go back to point 2, and think again.

4. Produce a sketch with numbers, then ask a trusted colleague or your supervisor to explain to you why it would not work reliably.

5. With your colleague's approval in writing, you can build the first prototype. If it fails, you are not alone. Your colleague also has an interest in fixing the design, and minimising the damage to your reputation.

Never work alone outside your job description or experience. Make it a team effort. You need others to blame, at the trial, for the errors.

 

[jrmichler]

In fact, it seems that in real-world applications, in 3D, with obstructions, one approaches the solution path more by trial and error than any analysis.

I once designed a four bar linkage. I first did a literature search looking for an analytical procedure, and found nothing that was of practical use. So that left trial and error, but not random trial and error. It was a series of steps:

1) Define the desired motion with a sketch
2) Write a Matlab program with pivot locations and bar lengths as inputs, and position and acceleration as outputs
3) Start with random inputs until I got something vaguely related to the desired output
4) Iterate towards the desired output shape
5) Rotate the entire assembly to get the desired output orientation
6) Scale the entire assembly to get the desired output magnitude
7) More iteration to fine tune the output shape
8) More iteration to reduce peak acceleration
9) Hand off to the design engineer to design actual parts, bearings, and drive mechanism
Following steps by the design engineer, machine shop, and R&D technician, plus suggestions from me:
10) Build a prototype
11) Test prototype
12) Redesign to strengthen parts that shook apart, redesign, build second prototype
13) Test 2nd prototype, redesign end effector, build third prototype
14) Repeat until Prototype #9 met all requirements for functionality, usability, ease of maintenance, and durability.

And that's how it works in the real world. We were able to start testing the complete machine at about Iteration #3 or #4, and got to Iteration #9 well before it was time to ship the machine. The project engineer's job is to identify long development paths far enough ahead of time, and see to it that they get enough priority, that the entire job will finish on time. This particular job was a small, apparently insignificant, subsystem in a 100 foot long machine. But very important to make the entire machine work.