Does increasing robotic arm's speed cost replayability?

Back in the 90's I worked on a robot for a pen manufacturer customer. They wanted to simulate nib wear by having a robot write cursive script continuously for hundreds of hours at a time, in a reproducible way.

If I remember correctly, the robot we developed was around 70cm tall, a tripod with the pen suspended on rods from near the apex. The motors were close to the top, one each for the x and y axis, using the long rod to amplify the speed and range of travel of the limited travel motors (voice coil, IIRC) we were using.

As others suggested, in order to be fast enough it had to be be incredibly lightweight. The low payload weight (just a pen) made this just about possible, but to get that speed sacrifices in positional accuracy had to be made with the technology available at the time.

These days we wouldn't have the control issues we did back then (integer PID parameters with the National instruments motor controller we were using, left our system at most marginally stable most of the time, forcing us to cut back the speed to retain stability) but the fundamental limitations of torque, speed, range of travel, precision and cost are always going to be difficult to balance, and unusual requirements in one of these aspects can push the component cost sky high.

There are lots more options available now though, from flexture stages, piezo walk or stack actuators, smaller, more precise lightweight linear motors, but all of these options are going to be expensive, far beyond most hobby budgets.

If you go for a Cartesian robot design, rather than a traditional 'arm', 50 micron accuracy is not too difficult/expensive if your range of movement is not too high. Even relatively cheap fused deposition 3d printers can get 10um step size (not accuracy). Much below 10 micron accuracy gets tough unless your range of movement is very restricted though.

An alternate approach is to reduce the mass and stiffness to enable higher accelerations, in combination with better sensing and control. For example, controlling the end-effector in relation to the target in sensor space instead of a global coordinate frame (which is likely arbitrary with respect to the task). The control scheme will have to allow for dynamic changes in the shape of the mechanism as it accelerates.

The robot arm can be made fast by making it light. Less mass to move allows higher acceleration which allows faster starts and stops.

The robot arm can be made precise by increasing stiffness. This is generally done by adding material.

Due to the slender nature and long unsupported nature of robot arms they are prone to movement and flex. Compared to CNC machines they are much less precise because of this.

Most robot arms on the market cannot get anywhere close to 0.01mm precision, let alone hit the same mark again. And this includes the smaller ones similar to what you are trying to build. (UR and Motoman smartseries)

I just checked the specs for a UR 3, repeatability (ability to hit the same mark multiple times) is +- 0.1mm.

If you can build something close to 0.01mm precision on a hobbyist budget I would be impressed.