Linkage Research

Owned by Mathieu Harter (Deactivated)
Last updated: Apr 25, 2021
5 min read

Introduction

When you google "6 axis arm" (or 5) there are a lot of pictures that look like the pictures below. They look very impressive with their smooth fancy casing, however those casings add unnecessary weight. Considering the fact that the rover has a weight restriction, and that a heavier arm means we need more powerful (aka more expensive and heavier) motors on the arm to move the extra weight, we probably don't want to do too much of this. The only advantage of the case (other than looking nice) is protecting the inner workings of the arm. The arms function exactly the same without the case.

Unsurprisingly, when you look at other teams' SAR videos, they don't really look the same. One big difference is that the URC arms all have the wiring external, whereas the fancy ones have all or the vast majority of wiring hidden inside the casing.

If we're considering aesthetics, wire management is a big part of it. Looking at the rover pictures above, the majority of them would look much sleeker/nicer without the wiring (in my opinion, at least). I think that instead of focusing on making fancy casing we should focus more on wire management, and aesthetics will come with that.

Anyway, that was a bit off topic, here are some common linkage types ("bone structures").

Common Linkage Structures

Note: These are not all mutually exclusive. Different segments of the arm can use completely different linkage styles.

DescriptionNotesExample
Thin frame on either side
  • Two thin pieces of material on either side of the segment (with nothing, just empty air/necessary supports, in between), just enough to connect to the actuator/previous segment and support the rest of the arm
  • Actuators and the next segment are located between the two frame pieces, making it symmetrical
  • Nowhere to hide wires or power transmission parts at all
  • Would be with a strong, lightweight material, but (I assume) would make for a very flimsy arm otherwise
  • Seems to be used more on lower segments, my assumption is that it would be harder to implement well higher up when you have more parts closer together
  • Actuator and everything contained in the joint module

Wider frame on either side (with lightening holes where possible/necessary)
  • I feel like this is just different enough from above to separate it
  • Similar to above with the symmetrical frame, empty center, etc
  • Wider frame is used to support motors, gears, etc instead of strictly being a link from one segment to the other
  • Seems more commonly used throughout the entire arm (as opposed to just the lower segments) than above
  • Provides more mounting points/opportunities to hide/manage wires than the thinner option
  • Also provides real estate for sponsor panels

Cylinder
  • Literally just a cylinder from one joint to the next
  • Seems more difficult to mount motors and stuff than the two-piece frame (?)
  • Wires can be routed through the center if it's hollow

Solid frame
  • Who needs flimsy sheet metal?
  • Solid, strong, heavy
  • We are not lifting heavy enough stuff to warrant a monster like this, and even if we were, I don't think we want to use the majority of our weight allowance on the arm


Fancy casing


(More of an optional addition than separate style)

  • A flimsier frame hidden underneath lightweight molded plastic to hide wiring and give it a sleek look
  • Also has the advantage of protecting the inner parts
  • Adds extra and mostly unnecessary weight, though

Skeletonized
  • Very light: most actuators moved to the bottom.
  • favorable center of gravity: all actuators near the bottom.
  • Sleek design, without the requirement for elegant curves
  • May be limiting to design with 6dof
  • poor design of the linkage bars may lead to an unacceptable tolerance stackup. This can be easily avoided with proper design and tolerancing.
  • Reduced wire length, everything near the bottom
  • More space at the wrist

uArm Swift - ROB-14341 - SparkFun Electronics


https://scholar.uwindsor.ca/cgi/viewcontent.cgi?article=5808&context=etd

Optimal Linkage Lengths

When looking at linkage lengths, a few things can be considered. The goal of a robotic arm is to execute a series of actions with as much precision and repeatability as possible. The speed at which it accomplishes these tasks also needs to be taken into account. Generally, having the joints closer to the end effector (and closer to each other) increases the precision of the positioning of the end effector. The further apart the joints are, the faster the arm will be (due to v = w x r). In many industrial robots, the wrist joints are as close as possible to the end effector to increase end effector positioning resolution, while the first two axes are as  close to the base as possible to give velocity to the arm.

Manipulability

A common metric to compare robotic arms is called manipulability. This is a rough measure of how difficult it is for the arm to move in a given direction. It is generally given with the following equation: 

Where J(q) is the Jacobian matrix for this manipulator. See the links and video below for more detail. Jacobian Matrices are explained in the arm theory.

https://engineerjau.wordpress.com/2013/05/04/advanced-robotics-manipulability-ellipsoids/

https://engineerjau.wordpress.com/2013/06/03/kinematic-manipulability-indicators-in-robotics/

Velocity Ellipsoid

Manipulability can be illustrated through the  use of a velocity ellipsoid. The previous measure is simply proportional to the volume of the ellipse. How to create the ellipsoid is shown in the image below (for 2D motion to keep it simple), taken from the following video