It probably doesn't matter so much whether it's 7.913 or 8.186, but it would be important to know the exact value for kinematics. One way to do that is to build an object very accurately, the other is to build inaccurately and then measure the result after the fact.

It's also interesting because competing actuators with strain-wave, cycloidal, or planetary gearboxes will state exactly what the ratio is. The actual gear teeth may not be spaced out perfectly around the circumference, but the number of teeth is an integer with an infinite number of zeros.

Getting that ratio nailed down also makes future designs more predictable I think

> That's why pro crews don't use gears and ropes. [...] Instead what you see is the motors right on the joints.

The answer here, as with so many things in robotics, is: It Depends.

UR10e robot arm that can lift a 4kg object with a reach of 1m and has sub-1mm repeatability? Strain wave gears in the base and shoulder joints, 100:1 ratio.

MIT Mini Cheetah robot dog that can do backflips? 6:1 planetary gearbox.

Shadow Hand with 20 degrees of freedom? Tendon driven, with the 20 motors in the forearm to keep the fingers slim.

Little dinky Huggingface SO-101? Servo motors, integrating 1:345 gearing with a series of 6 tiny brass gears.

Mid-price CNC milling machine, if you call that a robot? Really long ballscrews, driven by stepper motors.

> At high impulses deformations and elasticity throw the kinematics

Sure. Yet evolution has achieved astonishing kinematics with all manner of deformation and elasticity inherent to the materials, and also constantly changing physical properties, using low resolution data. We cannot build permanently lash free mechanical devices at reasonable cost and reasonable size/weight. Eventually, the answer must be pervasive real-time compensation throughout the kinematic model.

> Modeling the deformations and the elasticity is a computational no no.

Why? Nervous systems do this. That's why you can change your shoes and still walk upright.

In the video he mentions how the specific type of Dyneema cord he's using is well-suited for the application (compared to other kinds of rope/cord). It's particularly strong, light, and inelastic; a lot of climbing equipment uses a version of it for similar reasons.

more than 30 years ago I was writing code for a "robotic" device that used motors, directly on the joints.

the motors were so sloppy the company wasted a ton of money [0] having me write heuristics to tackle the errors they accumulated over several hours.

one of his whole points is that by using dyneema (rope), there's almost no elasticity at all in the capstans.

[0] relative to the cost of better motors

> Modeling the deformations and the elasticity is a computational no no. Instead what you see is the motors right on the joints.

That sounds like “It’s not wrong, we just don’t do it”. There are some amazing examples of imprecise drive systems compensated for by excellent control systems all over the world, for millions of years.

The point is that those decimal places don't have to be zeros. 7.893 is just as precise as 8.001.

I don't think the number of the gear ratio really matters, what matters is that you know what it actually is (since every IK calc depends on said ratio); 8:1 is probably arbitrary and/or looks nice & might simplify some stuff.