[nullc]

4 is still though fundamentally limited: you need a minimum six DOF to position all three translational and rotational freedoms. The human arm has 7, and I think a case can be made the smart software would reduce the problems from having only exactly as many as required. ... but not eliminate: the extra degree of freedom lets you "get out of your own way" when moving objects that are not zero size trough multiple positions :)

Perhaps 4 is enough for any specific application, but then again perhaps 3 is or 2. :P

I've never programmed a robot arm, but I've spent a fair amount of time using a seven axis faro arm (a coordinate measuring device, sort of the opposite of a robot arm) and it certainly takes some practice to avoid "cant move there from here without reorienting everything", it's easy to take for granted what our brains do automatically for us. :)

[IanCal]

Humans have 7 dof but we can't get into all positions, as I've found clearly today trying to reach things for my kids in the back seat of the car.

[IshKebab]

That's because of joint range of motion limitations. It's different to DoF limitations which is what was being discussed.

[IanCal]

The point is that you can achieve a lot without being able to access every position and the human arm having a lot of degrees of freedom doesn't necessarily mean it's more capable than a different arm with fewer.

[nullc]

Sure but why not, say, an XYZ or XYZT gantry instead?

There are a lot of downsides in 'arms' -- stacking all the axis hurts their speed, stiffnes, accuracy, increase complexity (e.g. in pathing, limiting speed, restricting to safe areas), limited reach.

I've always thought of them primarily as beneficial for flexibility at considerable cost, but if it's not 6dof then the flexibility isn't so great, then why not some other geometry?

[numpad0]

in simpler term: an object has position and rotation, and we're in 3D, so we need minimum 6 linearly independent parameters to be able to both point at a direction and be at a location at the same time.

Drone and helicopters has 4, and they are able to control max 4 of 6 parameters. Usually 3 positional + 1 rotational, and the rotatinal axis go first.