RoboMaster Engineer — SCARA Arm

Both shoulder motors are bolted to the tail, not to the arm. One turns the first link directly through its flange; the other drives a pulley on a short shaft, and a timing belt carries that torque out along the beam to the elbow. The links accelerate the payload and themselves — they never have to accelerate the actuators as well.

That belt shaft takes exactly two loads. Torque arrives through the flange, and the belt’s preload pulls on the pulley — purely radial, perpendicular to the axis. Nothing pushes along the shaft at all.

So the radial pull is what gets designed for, split between two bearings. Those two loads set the shaft diameter; the axial constraints set nothing, and only keep parts where they belong.

Idealize the link as a slender rod turning about its end (J = mL²/3), take α off the trapezoidal velocity ramp, and M = Jα with a 1.2 factor gives the requirement. Selection is graphical from there: the operating point has to land under the manufacturer’s curve.

And then the honest part. The motor actually fitted — an lk8016 — is more than twice the computed torque, because a competition robot lives outside its design case: it gets shoved, it hits walls. The calculation sets the floor; the margin is a judgement about the environment — and on the field that margin is what survived the collisions.

The link between the joints is a cantilever: the cube and the arm's own weight act out at the far end. What you want is the smallest deflection δ under that load, and for a given material that means the largest second moment of area of the section.

That quantity is I = ∫y² dA about the neutral axis — the plane through the section carrying no stress, tension above it and compression below. The y² is the whole story: material far from the neutral axis counts far more than material near it. Which is exactly what an I-beam does, and why it is so good in bending.

But this beam is not in pure bending. It is cranked, so a load at the end does not act through the beam's axis, and that offset raises a torque too. An I-beam is an open section: excellent in bending, poor in torsion. So the section has to be closed and still keep material out at the edges — and it has to be easy to clamp to: a round tube will not hold a fitting, and a square one chews up the brackets. A hollow octagonal tube was the best thing we could buy against all of that.

That settles the shape, not the material — an aluminum tube of the same section would carry the bending perfectly well.

The whole vehicle has a mass budget, so the quantity to maximize is specific stiffness: how much stiffness each gram buys.

Carry the bending and the torsion under a fixed mass budget, and a carbon-fiber octagonal tube wins it — 30 × 20 mm across the flats with a 1.5 mm wall, almost all of the material at the perimeter where the y² pays for it.

And it is fitted 30 mm axis vertical, standing in the plane the arm bends in. Run the section through the same integral both ways and it comes out at roughly 17,100 mm⁴ on the deep axis against 8,900 mm⁴ on the shallow one: the same tube turned ninety degrees loses about half its bending stiffness.

The prismatic axis has to cover a large height and place the cube precisely at the top of it — two requirements wanting two different machines. So it is staged:

• First stage — a cylinder, 400 mm. Fast, light, two useful states, no position feedback and none needed: it raises the whole arm structure.
• Second stage — a servo-driven ball screw, 350 mm. Slower and heavier per millimetre, but it holds a commanded position — this is what puts the arm at the right height for the exchange.

All 750 mm on the screw would have been accurate and far too slow; all of it on the cylinder, quick and unable to stop where it was told. The cylinder skips the dead height in the middle and the screw does the fine work — that split is the whole point.

Why the two carriage blocks are not level with each other

The SCARA platform hangs off the front of the carriage, so what it puts into the rails is weight plus an overturning moment, trying to tip the platform nose-down. There are two rails, one block on each, and the aluminium bracket joining them to the platform deliberately sets them at different heights.

The two rails sit 90 mm apart, and that separation is horizontal — it handles roll and yaw and does nothing for a moment acting about the axis running between them. Level with each other there is no separation along the rails, so no lever arm and no force couple: each block absorbs its share as rated pitch moment, far more restrictive than its load rating.

Staggering them by 24 mm along the rails turns that moment into a pair of forces — the higher block pulled off its rail, the lower one pushed into it, each seeing a normal load instead:

Level, the pair is limited by twice the block’s permissible pitch moment — 2 × 100 = 200 N·m for the HGH15CA blocks this uses. Staggered by 24 mm the limit is instead the static load rating acting on that lever arm — 23.47 kN × 0.024 m = 563 N·m. The same two blocks, close to three times the overturning capacity, for the price of a longer bracket.

Write that gain out and it reduces to d / (2 × M_pitch/C₀) — the stagger over twice the block’s own effective moment arm, which is 100 N·m / 23.47 kN = 4.3 mm here. That arm grows with block size, so the same 24 mm stagger returns 2.8× on an HGH15CA, 2.2× on an HGH20CA and 1.9× on an HGH25CA. The trick pays most exactly where you would otherwise be tempted to buy a bigger block.

And that is the cheap side of the trade: the bracket costs a little vertical space, while blocks large enough to take the moment head-on cost mass, money and room — on an axis whose whole job is to lift what it is bolted to.