BIOBUZZ Turret v8.1GB

The numbers behind the design, worked out step by step. Every value comes from the same model and simulations as the rest of this page, so they always agree. Each card starts with a question, explains every symbol, and ends with what the answer means for the robot. Most cards need only algebra and a little trigonometry. Card 2 uses one derivative (a calculus idea).

Decision	Why
Bought turret bearing: the goBILDA Gear-Driven Turret	The turret turns on goBILDA's Gear-Driven Turret (3208-0004-0001): an aluminum housing with a steel ball bearing, a 176-tooth gear ring on top, and a 64-tooth drive gear on a 312 rpm Yellow Jacket (2.75:1). It replaces our plywood base plate, printed ring gear and six rollers, so there is no roller preload to set and no printed ring to wear out, and the turret should wobble less. The ball comes up through its 105 mm bore. The housing bolts to the robot through the tapped holes in its flat sides, and the deck screws straight onto the gear ring.
Everything that turns stays within 201 mm of the turret axis	The lifter takes the back 2 in of the robot. With the turret axis 1 in forward of the robot's center, the lifter and the front of the 18 in start cube are both 203.2 mm from the axis. The modelled parts reach at most 201.1 mm, which leaves about 2 mm for build error, frame flex, plugs and cable ties. So the plan is that the turret can turn freely while the lifter is up. Until the built robot is measured with the lifter on it (turn the turret slowly through its full travel with the lifter up), keep the software limit as a backup. To get there, the flywheel motor sits lower and closer to the main shaft on a shorter 315 mm belt, and the side plates, the front crossbar and the camera moved back. The shot itself is unchanged: same wheels, same 3:1 belt ratio, same hood.
Compact at the start: 262 × 290 mm (10.3 × 11.4 in) and 193 mm tall above the robot surface	The rest of the robot needs room: a 2 in lifter at the back, the intake and the indexer that feeds balls up into the turret's center. The flywheel encoder (left) and the deck's home-magnet ear (right) set the width; the side plates (front) and the deck (back) set the length. That's with the upper wheel's arm closed, as it starts; a Nectar opens it to 308 mm. The turret bearing's housing is only 144 mm across, so nothing fixed sticks out past the turning parts. Its motor hangs under the left side, so the front and center under the turret stay free for the indexer, and the back stays free for the cables. The home switch sits on a small printed arm on the housing's front-right side.
Hood covers 55–80° (Pollen; 50–75° for Nectar)	For the real, tilted opening, the ideal angle goes from 74° close in to about 50° at 2.5 m (figures 1 and 2). For Pollen the hood stops at 55°. From 2 m out that's a little steeper than ideal, but it still leaves ±3.2% of speed room at 2.5 m (vs ±3.7% at 50°). For Nectar, the arm's geometry says 50–75°. But the swing-arm simulation says a Nectar really leaves about 6–10° steeper, about 58–85°. The bigger ball stays on the main wheel a little longer after it leaves the upper wheel, so it gets carried further up. Weaker or stronger springs barely change that. 59° still scores from 2.5 m, with ±2.5% of speed room instead of ±3.3%, and close shots are still covered. How far a Nectar opens the arm depends on how stiff the real balls are. So measure the balls and the real launch angle (see "Check before cutting"). Close in, the best angles match the 45° rule adjusted for a raised target (figure 7).
60:48 gear pair: the upper wheel runs about 6% slower	That gives mild backspin. In the simulation the typical (median) shot spins at about 70 rpm, but single shots range from slight topspin (spinning forward) to about 260 rpm of backspin. Backspin makes the ball settle on the cell's sloped floor instead of bouncing off the back wall. Bounce-outs still need testing with a mock cell.
Two linked flywheels, ball straight up between them	To launch steeply, the two wheels must sit nearly side by side at the pinch (the gap where they grip the ball), so the line between their centers is nearly level. The upper wheel also holds the ball against the main wheel, so no guide rollers are needed. The indexer should pop balls up at about 3 m/s. The upper wheel's underside then pushes the ball forward into the pinch, even with the hood flat (the shot slider in the 3D view plays the simulated path).
Belt to a jackshaft on the hood; gears to a swing arm on that jackshaft	Each stage pivots around the shaft that drives it. So no belt or gear pair changes its center distance (shaft-to-shaft spacing) when the hood tilts or the arm swings for a Nectar. The motor belt is tightened once, using the sliding adapter plate and the jack screw. The jackshaft belt has a fixed center distance, checked with a test plate.
Constant-force springs set the squeeze; the hard stop only catches worn balls	With a fixed stop, how hard the wheels grip depends on how squishy the ball is. With a spring force, new and worn balls get squeezed about equally hard. They still don't leave at the same speed. In the simulation, new and worn balls leave up to about 12–14% apart for Pollen (worn ones slower) and 9–10% for Nectar (there a new, firm Nectar is the slower one). Balls in one match wear about the same, so this mostly shows up between fresh practice balls and worn competition balls. Re-check the speed table with balls like the ones used in competition.
Flywheels geared 3:1 to about 8.5 m/s	Shots into the HIVE need the ball to leave at about 5–8 m/s (figure 1). The feed simulation shows the ball leaves at about the wheels' surface speed: a few percent faster for most balls, because the indexer's pop adds to it, but a worn Pollen at full speed slips and leaves up to 20% slower. So 8.5 m/s at the wheels covers every shot with some to spare. It's 85% of the motor's top speed. That leaves room for the motor to speed back up between shots (math cards 1 and 6).
Cables: the method is chosen after a bench test; the turret keeps room for every option	The ball goes up through the center, so a slip ring can't go there, and USB doesn't work well through slip rings anyway. Three ways are kept open: a cable loop that rolls under the base plate around the ball's path, a cable spiral around the same path, or a simple loop on the side with about ±120° of turning. So the base plate's center hole is 120 mm (ball and cables side by side), the space under the plate within about 95 mm of the center stays free, and the deck and base plate have zip-tie holes. A home switch lets the software know where the turret is, so it never winds the cables too far.
Plywood frame: two glued 1/8 in layers	Each frame plate (both side plates, both hood carriers and the deck) is two laser-cut 1/8 in (3 mm) Baltic birch plywood layers glued together, about 6.2 mm in all. Our Elegoo Phecda 20 W diode laser cuts 3 mm cleanly in one or two passes. A 1/4 in sheet takes more passes and leaves burnt, slanted edges. Two layers also let us turn the grain 90° between them, which makes the plate stronger in every direction. And we can hide things between the layers: nut pockets, and the lip of the servo insert. Why not thicker? The loads push along each plate, not through it. A rough estimate (the hood carrier treated as a simple arm with half the ball squeeze on its tip) says its tip bends about 0.04 mm in plywood and 0.005 mm in aluminum: plywood is about 8 times less stiff, but that's still far too small to affect the squeeze or the shot. It hasn't been tested yet. What needs thickness is the bearing seats, the screws and the knocks a robot takes, and 6 mm of plywood handles those. Every layer fits the laser's 400 × 400 mm bed and a 12 × 20 in sheet; a turret takes about 9 sheets.
Honeycomb pockets in the side plates	This season's game is BIOBUZZ, so the holes that make the side plates lighter are hexagons, like a honeycomb. Only whole hexagons are cut, with at least 6 mm of wood between them, so the pattern stays clean and strong. Every hole for a bolt, shaft or slot keeps a solid ring of wood around it.
Printed PA-CF parts, designed to be replaced	The swing arms, the motor adapter, the servo insert, the three belt pulleys (two 24T and one 48T) and the 18 shaft spacers are printed in PA-CF (carbon-fiber nylon). It's stiff and tough, and our Bambu Lab H2C and Creality K2 Plus can print it. Printing lets us make shapes nobody sells. The goBILDA part numbers of the pulleys are kept as backups.
Still bought where it matters most	The 16T motor pulley is metal (goBILDA makes it from aluminum and steel). Only about 6 of its teeth grip the belt, and it carries every spin-up. The hood gear (aluminum, 108 teeth) and the 20T hood pinion (steel) are bought too. If the servo ever pushes against an end stop, a rough estimate says the hood gear's teeth see about 140 MPa of stress. Printed teeth would likely break, and the hood gear is hard to reach. The Sonic Hubs hold the flywheels at 2000 rpm, so they're bought. So are the motors, encoder, servo, magnetic switch, bearings, shafts, belts, Gecko wheels, springs, collars, the acetal sync gears, screws and heat-set inserts. The team already owns the Limelight 3A.
Every in-season adjustment reachable with the turret fully assembled	The stop cams (for worn-ball squeeze) are set from the ball side. The motor belt tension is set from outside the motor-side plate, and the camera tilt from outside too. The hood zero and turret home are set in code. The model checks all this: it pushes a tool-sized cylinder out from every adjustment screw and flags it if anything is in the way.
Motor belt on an adjustable mount: an adapter plate that slides, and a jack screw	The 16T motor pulley has only about 6 teeth gripping the belt, and it carries the full torque (twisting force) of every spin-up. So this is the belt most likely to skip if it gets a little loose. With the adjustable mount, the fix takes a hex key and a minute instead of a new plate. It also makes motor and belt swaps quick. All four clamp bolts and the jack screw sit outside the pulley and belt, so you can reach them on the assembled turret. The jackshaft belt stays at a fixed spacing: it runs 1:1 with 12 teeth gripping and carries far less torque.
Optional front flair plate	A 3 mm panel for stickers, cut on a diode laser or printed, zip-tied to the front crossbar. It's decoration only, not a ROBOT SIGN. At about 155 mm wide it's narrower than the 165 mm a sign must be, and a sign on a turning turret would swing away from the referees. We put the two required red/blue ROBOT SIGNS on the chassis. Rule R401 allows any surface the referees can see, including the top, as long as the two signs are on opposite or neighboring sides, at least 90° apart.
Square nuts and button heads instead of threads and countersinks	Wood can't hold threads cut into it. So where a screw needs something to thread into, an M4 square nut (7 mm across, 2.2 mm thick) is pressed into a laser-cut pocket in one layer, with a drop of CA (super) glue, before the layers are glued. There are 8 in the deck's bottom layer for the L-bracket feet (each close pair shares one slot) and 2 in the motor-side plate's inner layer for the jack yoke. The printed motor adapter has 4 square-nut pockets for its clamp bolts. Flat-head screws would crush the wood, so there are no countersinks in the plates. The hood carriers form the walls of the ball's path, and a Nectar clears them by only about 4 mm. So each carrier's ball-side layer has 8.2 mm counterbores (round recesses), and button-head screws sit flush in them. Each stop-cam screw threads into a heat-set insert in its printed cam. The servo's screw holes are only about 4 mm from its body, too thin a strip for plywood. So the servo sits in a printed PA-CF insert: its lip is trapped between the servo-side plate's two layers, and the servo's 4 M3 screws go into M3 heat-set inserts in it (smaller M3 inserts leave more plastic next to the servo's opening than M4 ones would). The flywheel motor's four M4 × 8 button heads sit in the side plate's window. The model includes the heads and nuts of the structural bolts, the Sonic Hub screws and the spring-anchor screws, and checks that nothing hits them. It tests the hood steep, halfway and flat. It swings the upper-wheel arm from its stop to the bumper stop, 3° past the Nectar position. It also checks the cable ribbon every 10° of turret turn. Set screws sit inside their hubs. The camera's small screws and bolt threads aren't modeled.
Stacked springs and an arm bumper	The upper wheel is driven by gears from the jackshaft, so gripping a Nectar twists its arm open. With one spring per side, the simulation throws the arm wide open on nearly every Nectar, into the path of the spinning shaft spacers. The strongest narrow (12.7 mm) stock spring we found is 4 lb. So, as a trial, two 2.6 lb am-4666 springs are stacked on each drum. The arm then stays within about 29° in the simulation (with one per side: 81°). A cushioned bumper 3° past the Nectar position catches it if it ever goes further. The drum fits three; choose after testing real balls.
Rear ball guard	With the hood flat, or while the robot speeds up or brakes, a ball can bounce off the underside of the upper wheel and fall behind the feed hole, into the middle of the turret. A printed wall just behind the feed hole stops that. It's built onto the rear crossbar, so it adds one printed part and two screws. The feed simulation checked 2,700 cases: both balls, every hood angle, new to worn balls, and the robot speeding up or braking at up to 8 m/s². With the guard, no ball got behind the feed hole, and every ball popped up at 3 m/s or faster was shot. Without it, 36 got behind it, and 3 Nectars popped at 3 m/s or faster missed.
One flywheel motor	The robot holds at most 4 balls, and 3–4 shots per second is plenty. Speed: the longest Nectar shot (2.5 m) needs about 6.6 m/s at the ball. The simulation gets that with the wheels at about 7.3 m/s, 73% of the motor's free speed (its top speed with no load). Close shots use the default 8.5 m/s (85%). Torque: this was checked in a simulation of the wheels and balls together, with each shot's own wheel speed (only the cases below). Pollen barely slows the wheels. Four close Nectar vary by 1.6% at 4 per second and 0.2% at 3 per second. Hardest case: four long Nectar from 2.5 m with the hood at 25°. Each ball was checked against the speeds that score at its own simulated launch angle (about 57.7–58.2°, which scores from about 6.42 to 6.77 m/s). The wheels were set to 7.32 m/s so the first ball leaves in the middle of that range. At 4 per second the four leave at 6.60, 6.50, 6.47 and 6.47 m/s. All go in, but the last is only 0.8% above the slowest speed that scores. At 3 per second all four are within 0.3% of each other. So: the shooting code should fire each ball only when the encoder shows the wheels within ±1% of their target (a "firing gate"). In the simulation that settles at about 3.1 per second for long Nectar and 3.3 per second close in, with 0.4% spread. That gate isn't written yet; it's a requirement for the robot code. Other ranges, worn balls and mixed bursts still need checking on the real robot. The side plates have room for a second motor if faster long bursts are ever needed.
Through Bore Encoder V2 on the flywheel shaft	It counts 8192 steps per turn of the flywheel shaft. The motor's built-in encoder gives only 84 at that shaft, so this one measures speed about 100× more finely. The code can then wait until the wheels are exactly at speed before firing (a "ready-to-fire" check).
Limelight at the top front, 45° up	High cameras get blocked less. The tags face down. At 45°, the estimate says the camera can read the tags under our up-CELL from about 90% of the spots where we can score. A study at every degree from 20° to 50° finds the best between 43° and 49°, depending on how high the turret sits, and 45° is always within about 1.5 points of the best, so 45° is a good starting setting. At 35° it would be 73%, because it misses them up close, where they're almost overhead. These are geometry estimates (no other robots, no blur), not measured detection rates. The mount can be set from 25° to 50° (figure 5 compares every setting). Check this on a real field.
Main wheel low; hood servo and gear behind and below it	Keeps the turret at 193 mm tall at the start (hood steep), inside the 18″ starting cube (figure 3).
goBILDA parts with verified part numbers; shaft stacks generated by the model	Everything can be ordered and built. Every bearing, spacer and collar position comes from the same model as the plates.

	PA-CF (Bambu Lab PA6-CF)	PETG (Bambu Lab PETG HF)	TPU 95A (Bambu Lab TPU 95A HF)
Nozzle	hardened steel, 0.4 mm	any 0.4 mm	any 0.4 mm
Nozzle temp	280 °C (260–300)	245 °C (230–260)	230 °C (220–240)
Bed	110 °C (100–120), textured PEI + a thin coat of glue stick	70 °C (60–80), textured PEI	35 °C (30–45), with a brim
Chamber	door closed; chamber heat on, 50–60 °C	door closed; chamber heat off	door closed; chamber heat off
Speed	under 100 mm/s	the profile's speed	under 80 mm/s
Part fan	0–40%	the profile's setting (0–80%)	50–100%
Dry first	80 °C for 8–12 h, then print from a dry box	65 °C for 8 h if the roll was left open	70 °C for 8 h

Type	Parts	Layer	Walls, top/bottom, infill	How to place it	Why
gear	PA-CF_pulley_24t.stl ×2, PA-CF_pulley_48t.stl ×1	0.12 mm	6 walls, 100% infill (top/bottom don't matter when solid)	flat, teeth standing up; no supports	fine layers give clean teeth; solid so the teeth don't flex
solid	PA-CF_guide_spacer.stl ×4, PA-CF_cf_axle.stl ×2, PA-CF_stop_cam.stl ×2, PETG_arm_bumper_core.stl ×2, PETG_encoder_sleeve.stl ×1, PETG_encoder_bracket_leg.stl ×2, PA-CF_spacer_1mm.stl ×3, PA-CF_spacer_2mm.stl ×3, PA-CF_spacer_3mm.stl ×1, PA-CF_spacer_4mm.stl ×3, PA-CF_spacer_6mm.stl ×1, PA-CF_spacer_7mm.stl ×1, PA-CF_spacer_8mm.stl ×1, PA-CF_spacer_9mm.stl ×2, PA-CF_spacer_12mm.stl ×3	0.16 mm	100% infill (top/bottom don't matter when solid)	flat end down	clamped under bolts or setting a stop: solid plastic doesn't squash over a season
strong	PA-CF_swing_arm_servo.stl ×1, PA-CF_swing_arm_motor.stl ×1, PA-CF_servo_insert.stl ×1, PA-CF_motor_adapter.stl ×1, PA-CF_deck_shim.stl ×1, PA-CF_switch_arm.stl ×1, PETG_cf_spring_drum.stl ×2, PETG_l_bracket.stl ×4, PETG_crossbar.stl ×2, PA-CF_cf_clamp.stl ×2, PA-CF_cf_anchor.stl ×2, PETG_motor_lug.stl ×1, PETG_motor_yoke.stl ×1, PETG_limelight_mount.stl ×1, PETG_encoder_bracket.stl ×1, PETG_home_flag.stl ×1	0.20 mm	5 walls, 7 top + 6 bottom layers (~1.4 / 1.2 mm), 50% gyroid	the largest flat face down; supports only where the slicer insists	takes load and holds heat-set inserts (5 walls = solid plastic around each insert)
light	PETG_rear_guard.stl ×1	0.20 mm	3 walls, 4 top + 3 bottom layers (~0.8 / 0.6 mm), 20% gyroid	flat on the bed	big and lightly loaded: fewer walls save hours and filament
soft	TPU_arm_bumper_ring.stl ×2	0.20 mm	100% infill	flat	TPU stays soft at any infill; solid gives the bumper an even feel

Adjustment	How to reach it on the assembled turret
Worn-ball squeeze (stop cams)	2.5 mm hex key from the ball side, through the ball's path. Loosen, turn the cam, retighten.
Camera tilt	Two lock screws, one on the outside of each side plate. Move both to the matching holes (25–50° in 5° steps).
Turret motor swap	From the left side, under the turret: the motor and its 64T gear come off goBILDA's motor mount without touching the deck. The gear mesh is fixed by the mount, so there is nothing to set.
Hood servo swap	From outside the servo-side plate. Take out the 4 M3 × 8 screws that hold the servo in its printed insert's heat-sets, and slide the servo out. The insert stays in the plate.
Hood zero, turret home	In code: a servo offset, and the home switch reading.
Firing gate, ball-wear offset	In code (not written yet). Firing gate: fire only when the encoder shows the wheels within ±1% of target speed. This spaces out long Nectar shots. It needs the indexer to hold the next ball and release one when told (see "What the indexer must do"). Ball-wear offset: one speed multiplier per ball type. Adjust it at each event with a few shots on the practice field, because practice balls are fresher than competition balls.
Spring count (1–3 per side)	Set once, after the ball squeeze test, not during the season. Changing it means taking the arm's spring ends off the anchor blocks, which sit between the hood carriers and the side plates. The spring-end screw is hidden behind the upper wheel's 48T gear (servo side) and its shaft collar (motor side). So slide those off the upper shaft first, with the hood raised to about 25°. (At 0° the gear's hub hits the servo-side plate as it slides out.)
Motor belt tension	From outside the motor-side plate: 1. Loosen the 4 clamp bolts about a quarter turn (2.5 mm hex key). 2. Turn the jack screw at the front (2.5 mm hex key): clockwise to tighten, counter-clockwise to loosen. Stop when the belt is just tight enough not to skip (see the motor belt test below), then turn about 1/8 turn more. If the lug touches the yoke before that, the mount is at the end of its travel: tell the design lead (the motor position needs a trim), and don't force it. 3. Retighten the clamps. 4. Put blue threadlocker on the clamps and the jack screw. Draw a paint line across the lug and the side plate, so you can see at a glance if it ever moves.
Jackshaft belt tension	None needed. The shafts are a fixed distance apart, set once with the belt test plate before cutting.

From the opening	Square-on	30° to the side	60° to the side
0.50 m	83°, ±5.9% 84°, ±5.3%	83°, ±6.2% 84°, ±5.4%	robot can't be here (frame base)
0.75 m	75°, ±5.2% 74°, ±4.9%	73°, ±4.9% 76°, ±4.6%	83°, ±6.5% 84°, ±5.6%
1.00 m	69°, ±4.8% 70°, ±4.5%	69°, ±4.5% 70°, ±4.2%	83°, ±5.3% 74°, ±4.7%
1.50 m	61°, ±4.4% 62°, ±4.2%	63°, ±4.2% 62°, ±3.9%	63°, ±4.2% 60°, ±3.9%
2.00 m	55°, ±4.1% 58°, ±3.4%	57°, ±3.9% 58°, ±3.2%	57°, ±3.7% 58°, ±3.4%
2.50 m	55°, ±3.2% 58°, ±2.7%	55°, ±3.2% 58°, ±2.7%	55°, ±3.2% 58°, ±3.0%

Requirement	Why
Hold the next ball, then release exactly one when the code says. While it waits, the ball must not touch the flywheels.	This is the mechanical half of the firing gate. The code fires only when the encoder shows the wheels within ±1% of target speed, which slows long Nectar shots to about 3 per second. A belt that feeds whenever a ball is there can't be controlled this way.
Pop each ball up at 3 m/s or faster (measured 30 mm below the turret bearing's bottom), the same every time, for both balls.	The feed simulation checked every hood angle from 0° to 25° (in 5° steps), pops from 1.6 to 4.4 m/s, new, medium and worn balls, and the robot speeding up or braking at up to 8 m/s². With the rear guard, every ball popped at 2.4 m/s or faster is shot in every one of those cases, so 3 m/s leaves some margin. A pop that's too slow just falls back down the feed hole, and the indexer can pop it again. The guard stops balls from dropping behind the feed hole. Test the real indexer with the hood flat and the robot moving.
Have the next ball ready 0.25 s after a shot, and keep the delay from "fire" to the ball reaching the wheels the same every time. Measure it.	0.25 s is the fastest rate (4 per second) the design plans for. A steady delay lets the code time the release.
Feed straight up the turret's center line, centered, through the turret bearing's 105 mm bore, with the turret facing any direction (±190°). The path must fit a 91 mm Nectar (it clears the bore by only 6.8 mm each side, so the indexer must center it) and still keep a 71 mm Pollen centered.	The indexer is on the robot and doesn't turn with the turret, so the ball has to arrive right on the line the turret spins around.
Tell the code which ball is next: a sensor at the gate that sees a ball is there, and a color sensor (Pollen is yellow; Nectar is red or blue).	Pollen and Nectar need different wheel speeds and hood angles. The code sets both, and waits for the hood to move, before it opens the gate.
Fit under the turret together with the drivetrain and intake: 258 mm (10.2 in) below the robot surface the turret bearing bolts to. Store up to 4 balls behind the gate.	The 18 in starting height (figure 3).
Count toward the motor and servo limit (rule R503: 8 motors and 8 servos for the whole robot).	The turret already uses 2 motors (flywheel and turret) and 1 servo (hood).

What	From	Cost
Parts and materials	goBILDA	$607.42
Parts and materials	REV Robotics	$65.50
Parts and materials	AndyMark	$43.20
Parts and materials	McMaster-Carr	$79.29
Parts and materials	Amazon	$72.29
Parts and materials	Bambu Lab	$42.99
Parts and materials	Hardware store	$1.00
Total		$911.69

Part	Buy	Price	Line
3208-0004-0001 Gear-Driven Turret (2.75:1 Ratio, 105mm ID)	1 × each	$169.99	$169.99
5203-2402-0001 5203 Series Yellow Jacket Motor (1:1 Ratio, 24mm Length 8mm REX® Shaft, 6000 RPM, 3.3 - 5V Encoder)	1 × each	$54.99	$54.99
5203-2402-0019 5203 Series Yellow Jacket Planetary Gear Motor (19.2:1 Ratio, 24mm Length 8mm REX Shaft, 312 RPM, 3.3 - 5V Encoder)	1 × each	$54.99	$54.99
2000-0025-0002 2000 Series Dual Mode Servo (25-2, Torque)	1 × each	$36.99	$36.99
1922-0025-0036 8mm REX® Servo Shaft (25 Tooth Spline, 36mm Length)	1 × each	$10.99	$10.99
2303-4008-0020 2303 Series Steel, MOD 0.8 Pinion Gear (8mm REX® Bore, 20 Tooth)	1 × each	$10.59	$10.59
2302-0032-0108 2302 Series Aluminum, MOD 0.8, Hub Mount Gear (32mm Bore, 108 Tooth)	1 × each	$16.99	$16.99
2312-0414-0060 60 Tooth Hub-Mount Gear (MOD 0.8, 4mm Thick Acetal)	1 × each	$3.79	$3.79
2312-0414-0048 48 Tooth Hub-Mount Gear (MOD 0.8, 4mm Thick Acetal)	1 × each	$3.19	$3.19
3417-4008-0016 3417 Series 5mm HTD Pitch Set-Screw Pinion Timing Belt Pulley (8mm REX® Bore, 16 Tooth)	1 × each	$9.99	$9.99
3412-0009-0410 5mm Pitch HTD Timing Belt (9mm Width, 410mm Pitch Length, 82 Tooth)	1 × each	$6.09	$6.09
3412-0009-0315 5mm Pitch HTD Timing Belt (9mm Width, 315mm Pitch Length, 63 Tooth)	1 × each	$5.39	$5.39
REV-11-3174 Through Bore Encoder V2	1 × each	$48.00	$48.00
3613-0014-0096 GripForce Gecko™ Wheel (14mm Bore, 96mm Diameter, 30A Durometer)	3 × each	$9.99	$29.97
3613-0014-0072 GripForce Gecko™ Wheel (14mm Bore, 72mm Diameter, 30A Durometer)	3 × each	$8.99	$26.97
1309-0016-4008 1309 Series Sonic Hub (8mm REX® Bore)	6 × each	$7.99	$47.94
2106-4008-2400 8mm REX® Shaft with E-Clip (Stainless Steel, 240mm Length)	1 × each	$8.89	$8.89
2106-4008-1680 8mm REX® Shaft with E-Clip (Stainless Steel, 168mm Length)	2 × each	$7.19	$14.38
1611-0514-4008 1611 Series Flanged Ball Bearing (8mm REX® ID x 14mm OD, 5mm Thickness) - 2 Pack	5 × 2-pack	$5.99	$29.95
2910-0920-4008 2910 Series Aluminum Clamping Collar (8mm REX® ID x 20mm OD, 9mm Length)	3 × each	$4.99	$14.97
3122-0002-0001 Limelight 3A Smart Camera	0 × each	$189.00	$0.00
am-4666 0.5 in. Wide 30 in. Long Constant Force Spring	6 × each (one 0.5in x 30in spring)	$7.20	$43.20
REV-31-1462 Magnetic Limit Switch	1 × each (switch + 2 magnets per BOM)	$17.50	$17.50
2800-0004-0012 M4 x 12 socket head (need 36: deck to turret bearing 8, crossbars + rear guard tube 6, rear guard anti-turn 2, camera 4, L-bracket feet 8, ...)	1 × 25-pack (250-pack $17.99)	$3.59	$3.59
2800-0004-0016 M4 x 16 socket head (need 2)	1 × 25-pack (250-pack $18.99)	$3.79	$3.79
2800-0004-0020 M4 x 20 socket head (need 8)	1 × 25-pack	$3.99	$3.99
2800-0004-0030 M4 x 30 socket head (need 2: encoder ears, nyloc behind)	1 × 25-pack	$4.29	$4.29
2800-0004-0050 M4 x 50 socket head (need 2: encoder legs, nyloc outside)	1 × 25-pack	$5.19	$5.19
91290A192 M4 x 80 socket head, black-oxide alloy 12.9 (need 8: Gecko stacks)	1 × 10-pack	$9.31	$9.31
2802-0004-0008 M4 x 8 button head (need 6: flywheel motor 4, spring ends 2)	1 × 25-pack	$3.19	$3.19
2802-0004-0010 M4 x 10 button head (need 14: sync gears 8, motor clamps 2, stop cams/bumpers 4)	1 × 25-pack	$3.39	$3.39
2802-0004-0016 M4 x 16 button head (need 5: hood gear 4, motor jack screw 1)	1 × 25-pack	$3.79	$3.79
2802-0004-0020 M4 x 20 button head (need 6: 48T pulley 4 + clamp 2)	1 × 25-pack	$3.99	$3.99
2802-0004-0025 M4 x 25 button head (need 10: robot mount 8, spring-drum sleeves 2)	1 × 25-pack	$4.19	$4.19
2802-0004-0045 M4 x 45 button head (need 4: hood guide bolts)	1 × 25-pack	$4.89	$4.89
91294A192 M4 x 12 flat head (need 2: spring anchors)	1 × 100-pack	$6.38	$6.38
2812-0004-0007 M4 nylock nut (need 20)	1 × 25-pack (250-pack $14.99)	$2.99	$2.99
97258A102 M4 thin square nut, DIN 562, 18-8 stainless (7 mm wide, 2.2 mm high) (need 14: deck 8, jack yoke 2, motor adapter 4)	1 × 50-pack	$14.00	$14.00
94459A150 M4 brass heat-set insert for plastic, 4.7 mm long, 5.6 mm hole (need 35)	1 × 50-pack	$10.82	$10.82
94459A130 M3 brass heat-set insert for plastic, 4.3 mm long, 4.0 mm max hole (need 4: hood servo ears in the printed servo insert)	1 × 50-pack	$10.91	$10.91
91292A123 M3 x 20 socket head, 18-8 SS (need 4: limit switch 2, home magnet 2)	1 × 100-pack	$9.69	$9.69
2800-0003-0008 M3 x 8 socket head (need 4: hood servo ears)	1 × 6-pack	$3.09	$3.09
93625A223 M3 x 0.5 nylon-insert locknut, black-oxide 18-8 SS (need 4: switch 2, magnet 2)	1 × 10-pack	$5.40	$5.40
91390A100 M3 x 6 cup-point set screw, alloy steel, DIN 916 (need 2: printed 24T pulleys)	1 × 100-pack	$7.10	$7.10
91828A211 M3 hex nut, 18-8 stainless, 5.5 mm wide x 2.4 mm high, DIN 934 (need 2: printed 24T pulleys)	1 × 100-pack	$5.68	$5.68
B08429ZRB1 Woodpeckers 3 mm (1/8 in) Baltic birch plywood, 12 x 20 in, B/BB grade, box of 20 (need ~10: 9 for the plates + fit/belt test pieces)	1 × box of 20 sheets	$67.31	$67.31
72100 Bambu Lab PA6-CF filament, Black, 1.75 mm, 0.5 kg with spool (need ~300 g)	1 × 0.5 kg spool	$42.99	$42.99
B0002YQ378 Titebond III Ultimate Wood Glue, 4 oz	1 × 4 oz bottle	$4.98	$4.98
generic 1/8 in x 36 in hardwood dowel (cut into 6 mm alignment pins)	1 × each	$1.00	$1.00

Type	Used for	Layer	Walls / infill	How to place it
plate	base plate, deck, side plates, hood carriers, swing arms	0.20 mm	4 walls, 30% gyroid	flat on the bed
gear	gears, pulleys, the turret ring, hubs, collars, servo shaft	0.12 mm	6 walls, 100% infill	flat, teeth vertical; no supports
shaft	hex shafts	0.16 mm	100% infill	lying on a flat side of the hex, with a brim
wheel	the 96 mm and 72 mm Gecko wheel stand-ins	0.20 mm	3 walls, 15% infill	flat
dummy	motors, servo, encoder, camera, home switch (look only)	0.28 mm	2 walls, 10% infill	any; supports where the slicer asks
standard	everything else	0.20 mm	3 walls, 25% infill	the flattest face down

Step	File	Qty	Print as	Real part (buy later)
01 · Base ~13 g	PETG_switch_arm	1	standard	the real one is this print (PA-CF)
PETG_home_switch_standin	1	dummy	REV-31-1462
02 · Ring and deck ~152 g	PETG_deck	1	plate	deck_L1.dxf + deck_L2.dxf (plywood)
PETG_deck_shim	1	standard	the real one is this print
PETG_home_flag	1	standard	the real one is this print
03 · Frame ~351 g	PETG_side_plate_servo	1	plate	side_plate_servo_L1.dxf + side_plate_servo_L2.dxf (plywood)
PETG_side_plate_motor	1	plate	side_plate_motor_L1.dxf + side_plate_motor_L2.dxf (plywood)
PETG_servo_insert	1	standard	the real one is this print, in PA-CF
PETG_l_bracket	4	standard
PETG_crossbar	2	standard
PETG_rear_guard	1	standard
04 · Flywheel motor mount ~45 g	PETG_motor_adapter	1	standard	the real one is this print, in PA-CF
PETG_motor_lug	1	standard
PETG_motor_yoke	1	standard
PETG_flywheel_motor_standin	1	dummy	5203-2402-0001
05 · Hood and shafts ~606 g	PETG_hood_carrier_servo_side	1	plate	hood_carrier_servo_L1.dxf + hood_carrier_servo_L2.dxf (plywood)
PETG_hood_carrier_motor_side	1	plate	hood_carrier_motor_L1.dxf + hood_carrier_motor_L2.dxf (plywood)
PETG_swing_arm_servo_side	1	plate	PA-CF_swing_arm_servo.stl / PA-CF_swing_arm_motor.stl (the real ones are prints)
PETG_swing_arm_motor_side	1	plate	PA-CF_swing_arm_servo.stl / PA-CF_swing_arm_motor.stl (the real ones are prints)
PETG_hood_gear_108T	1	gear	2302-0032-0108
PETG_servo_pinion_20T	1	gear	2303-4008-0020
PETG_servo_shaft	1	gear	1922-0025-0036
PETG_hood_servo_standin	1	dummy	2000-0025-0002
PETG_gear_60T	1	gear	2312-0414-0060
PETG_gear_48T	1	gear	2312-0414-0048
PETG_pulley_24T	2	gear	3417-4008-0024
PETG_pulley_16T	1	gear	3417-4008-0016
PETG_pulley_48T	1	gear	3415-0014-0048
PETG_sonic_hub	5	gear	1309-0016-4008
PETG_gecko_96	3	wheel	3613-0014-0096
PETG_gecko_72	3	wheel	3613-0014-0072
PETG_collar	3	gear	2910-0920-4008
PETG_shaft_main_239mm	1	shaft	2106-4008-2400
PETG_shaft_jack_upper_159mm	2	shaft	2106-4008-1680
PETG_bearing_1611_standin	10	standard	1611-0514-4008 (2-pack)
PETG_spacer_1mm	3	standard	1500-0010-0008
PETG_spacer_2mm	3	standard	1522-0010-0020
PETG_spacer_3mm	1	standard	1522-0010-0030
PETG_spacer_4mm	3	standard	1522-0010-0040
PETG_spacer_6mm	1	standard	1522-0010-0060
PETG_spacer_7mm	1	standard	1522-0010-0070
PETG_spacer_8mm	1	standard	1522-0010-0080
PETG_spacer_9mm	2	standard	1522-0010-0090
PETG_spacer_12mm	3	standard	1522-0010-0120
PETG_stop_cam	2	standard
PETG_cf_spring_drum	2	standard
PETG_cf_axle	2	standard
PETG_guide_spacer	4	standard
PETG_cf_anchor	2	standard
PETG_cf_clamp	2	standard
PETG_arm_bumper_core	2	standard
PETG_arm_bumper_ring	2	standard
06 · Last ~120 g	PETG_encoder_bracket	1	standard
PETG_encoder_bracket_leg	2	standard
PETG_encoder_sleeve	1	standard
PETG_limelight_mount	1	standard
PETG_front_plate	1	standard
PETG_encoder_standin	1	dummy	REV-11-3174
PETG_limelight_standin	1	dummy	3122-0002-0001

1 · How fast is the flywheel's surface?

The motor spins at [[motor_rpm]] rpm. How fast does the surface of the wheel move? That's roughly how fast the ball leaves.

The belt runs from a [[pul_small]]-tooth pulley on the motor to a [[pul_big]]-tooth pulley on the wheel shaft. The belt moves both pulleys by the same number of teeth. So the big pulley turns slower, by the ratio of the tooth counts:

\[ G = \frac{N_\text{big}}{N_\text{small}} = \frac{[[pul_big]]}{[[pul_small]]} = [[gear]] \qquad n_\text{wheel} = \frac{[[motor_rpm]]\ \text{rpm}}{[[gear]]} = [[n_wheel]]\ \text{rpm} \]

A point on the rim moves at \( v = \omega r \). Here \( \omega \) is the spin rate in radians per second (\( \omega = 2\pi n / 60 \)), and \( r \) is the radius. The wheel is 96 mm across, so \( r = [[r1_mm]] \) mm:

\[ v_\text{free} = \frac{2\pi \cdot [[n_wheel]]}{60} \times [[r1_m]]\ \text{m} = [[v_free]]\ \text{m/s} \]

What it means: we aim for [[v_target]] m/s, which is [[pct_free]]% of the free speed (the top speed with no load), or about [[n_target]] rpm at the wheel. A motor can't hold its free speed while it's doing work. Aiming lower leaves room for a weaker battery, and for the speed control to catch up after each shot.

2 · Where the 45° rule comes from

Which launch angle reaches a target with the least speed? (This card ignores air drag. The simulations include it.)

Launch from the starting point (the origin) at speed \( v \) and angle \( \theta \). The target is \( x \) meters across and \( y \) meters up. Gravity is \( g = 9.81\ \text{m/s}^2 \). The height of the ball at distance \( x \) is:

\[ y = x\tan\theta - \frac{g x^2}{2 v^2 \cos^2\theta} \]

Solve for \( v^2 \) and use \( 2\cos^2\theta = 1 + \cos 2\theta \) and \( 2\sin\theta\cos\theta = \sin 2\theta \):

\[ v^2 = \frac{g x^2}{x \sin 2\theta - y\cos 2\theta - y} \]

The smallest \( v \) comes from the biggest bottom part of the fraction (the denominator). To find where it's biggest, set its derivative (its rate of change as \( \theta \) changes) to zero:

\[ 2x\cos 2\theta + 2y \sin 2\theta = 0 \;\;\Rightarrow\;\; \tan 2\theta = -\frac{x}{y} \]

Solve that for \( \theta \). (Pick the answer that makes the denominator biggest, not smallest.)

\[ \theta^* = 45^\circ + \tfrac{1}{2}\varphi, \qquad \varphi = \arctan\frac{y}{x} \]

Here \( \varphi \) is the angle of a straight line from the launcher up to the target. On level ground \( y = 0 \), so \( \varphi = 0 \) and \( \theta^* = 45^\circ \). That's the coach's rule. The least speed works out to \( v_\text{min}^2 = g\,(y + \sqrt{x^2 + y^2}) \).

Our case: a cell [[ex_x]] m away whose opening is [[ex_y]] m above the launcher:

\[ \varphi = \arctan\frac{[[ex_y]]}{[[ex_x]]} = [[ex_phi]]^\circ \qquad \theta^* = 45^\circ + \frac{[[ex_phi]]^\circ}{2} = [[ex_theta]]^\circ \] \[ v_\text{min} = \sqrt{9.81\,([[ex_y]] + \sqrt{[[ex_x]]^2 + [[ex_y]]^2})} = [[ex_vmin]]\ \text{m/s} \]

What it means: the full simulation, with drag and the real tilted opening, picks [[ex_best]]°, almost exactly what the rule says. There's a bonus. Near the best angle, the needed speed barely changes, because the speed curve is flat at its lowest point. Being 5° off (either way) needs only [[ex_v_p5]] m/s, [[ex_pct5]]% more speed. So a small hood error costs little: the flywheel speed only has to change a little to make up for it. (This card ignores drag and treats the opening as a point. It doesn't promise that a shot at the same speed still scores.)

3 · Why a few percent of speed matters

If the ball leaves [[sens_pct]]% too fast, how far off does it land?

On level ground, a thrown object's range (how far it goes) is \( R = v^2 \sin 2\theta / g \). Range grows with the square of speed. For small changes, \( d(v^2) = 2v\,dv \), so a speed error counts double:

\[ \frac{\Delta R}{R} \approx 2\,\frac{\Delta v}{v} \qquad [[sens_pct]]\%\ \text{speed error} \;\Rightarrow\; [[sens_range]]\%\ \text{range error} \]

At [[sens_d]] m, [[sens_range]]% is [[sens_cm]] cm, about the size of the part of the opening a ball can actually use.

What it means: figure 2 shows the real opening allows about ±3.2–5% for Pollen, from 2.5 m in to 0.75 m (Nectar is a little tighter). So the exit speed (how fast the ball leaves) has to stay within a few percent from shot to shot, and as balls wear. That's the job of the encoder, the constant-force springs and the flywheel's stored energy (cards 5 and 6).

4 · Backspin from a gear pair

How much spin do the [[zj]]:[[zs]] gears put on the ball?

The jackshaft turns at the same speed as the main wheel (1:1 belt). Its [[zj]]-tooth gear drives a [[zs]]-tooth gear on the upper wheel, so the upper shaft turns \( [[zj]]/[[zs]] = 1.25 \) times as fast. The upper wheel is smaller, though (radius [[r2_mm]] mm vs [[r1_mm]] mm). Comparing surface speeds \( v = \omega r \):

\[ \frac{v_\text{upper}}{v_\text{main}} = \frac{[[zj]]}{[[zs]]}\times\frac{[[r2_mm]]}{[[r1_mm]]} = [[ratio]] \qquad \Delta v = (1 - [[ratio]])\times [[v_target]] = [[dv]]\ \text{m/s} \]

The ball is squeezed between two surfaces moving at different speeds, so it rolls. Its spin is about the speed difference divided by its diameter \( d \) (the distance across the ball):

\[ \omega_\text{ball} \approx \frac{\Delta v}{d} = \frac{[[dv]]}{0.0711} = [[spin_p_rad]]\ \text{rad/s} \approx [[spin_p]]\ \text{rpm (Pollen)}, \quad [[spin_n]]\ \text{rpm (Nectar)} \]

What it means: the contact simulation (with the real swing arm) gives about +50 rpm on average across all its shots, about the same. That's gentle backspin. It's enough to help the ball settle on the cell's sloped floor instead of bouncing out, but not enough to bend its flight.

5 · How hard the wheels squeeze

Stacked constant-force springs pull on the upper wheel's arm. How much force reaches the ball?

The arm pivots on the jackshaft, like a seesaw. The wheel's axle is [[arm_l]] mm from the pivot. The springs attach at the arm's tail, [[arm_tail]] mm from it. The arm stays still when the turning effects on each side balance (turning effect, or moment = force × distance):

\[ F_\text{pinch} \times [[arm_l]] = [[cf_total]]\ \text{N} \times [[arm_tail]] \;\;\Rightarrow\;\; F_\text{pinch} \approx [[pinch]]\ \text{N} \]

Here [[cf_total]] N is four springs of [[cf_n]] N (two stacked on each side).

A normal spring pushes harder the more it stretches (\( F = kx \)), so a big, firm ball would get squeezed harder than a small or worn one. A constant-force spring pulls the same amount wherever the arm is.

What it means: new and worn balls get about the same squeeze force. They don't get squashed the same number of millimeters: a softer ball squashes further under the same force. This simple lever math treats the forces as square (at 90°) to the arm. At the springs' real angles, the pull is a little lower when the arm is swung out. The gear drive also adds its own twist ("How it works", 4). So the real grip varies more than this suggests. In the simulation, new and worn balls leave within about 12–14% of each other for Pollen and 9–10% for Nectar.

6 · Stored energy: why one motor is enough

Each shot slows the wheels down. How long does the motor take to bring them back?

A spinning wheel stores energy \( E = \tfrac12 I\omega^2 \). Here \( I \) is the moment of inertia: how hard it is to speed up or slow down the spin. For this turret it's all the spinning parts together, measured at the main shaft: \( I = [[I]]\times10^{-4}\ \text{kg·m}^2 \). At full speed, \( \omega_0 = [[v_target]]/[[r1_m]] = [[w0]]\ \text{rad/s} \):

\[ E_0 = \tfrac12 \,( [[I]]\times10^{-4})\,([[w0]])^2 = [[E0]]\ \text{J} \]

A Nectar leaves with kinetic energy (energy of motion) \( \tfrac12 m v^2 = \tfrac12 (0.0413)(8.3)^2 = [[ke]]\ \text{J} \). In the simulation, each Nectar drops the wheels to [[v_dip]] m/s (\( \omega_1 = [[w1]] \) rad/s), which takes out:

\[ \Delta E = \tfrac12 I\,(\omega_0^2 - \omega_1^2) = [[E_take]]\ \text{J} \]

That's about [[take_x]]× the ball's own energy. Not all of the difference is wasted. Some goes into the ball's spin, some into squashing it and into slipping, and the motor adds energy during the shot. So this simple count can't split it up exactly. It only shows that one shot takes a noticeable bite out of the flywheel's energy.

A DC motor's power depends on its speed: \( P = \tau_s\,\omega_m\,(1 - \omega_m/\omega_f) \). Here \( \tau_s = [[tau_s]] \) N·m is the stall torque (twisting force when held still) and \( \omega_f = [[w_f]] \) rad/s is the free speed (top speed with no load). Power peaks at [[p_max]] W at half speed. A flywheel runs fast, at [[frac_hi]] of free speed, where the motor only makes [[p_hi]] W. That rises to [[p_lo]] W when the wheel slows after a shot. Using an average of about [[p_avg]] W:

\[ t_\text{recover} \approx \frac{\Delta E}{\bar P} = \frac{[[E_take]]\ \text{J}}{[[p_avg]]\ \text{W}} = [[t_rec]]\ \text{s} \;\;\Rightarrow\;\; \text{about } [[rate]]\ \text{Nectars per second} \]

What it means: this is a rough estimate. It assumes the motor gives its average power the whole time. It also ignores the energy the motor adds while the ball is still between the wheels. The simulation includes both. It shows four close Nectars leave within [[spread3]]% of each other at 3 per second, and within [[spread4]]% at 4 per second. The robot holds 4 balls, and 3–4 per second is plenty. So one motor does the job, with the firing gate spacing out long shots (see "Design decisions").

7 · How fast and how precisely the turret aims

How quickly can the turret swing around, and how finely can it point?

A [[pinion]]-tooth pinion (small gear) on the motor drives the [[ring]]-tooth ring gear: \( [[ring]]/[[pinion]] = [[ratio_t]]{:}1 \). The 312 rpm motor turns the turret at \( 312/[[ratio_t]] = [[turret_rpm]] \) rpm, a half turn in about [[t180]] s (not counting the time to speed up).

The motor's encoder counts [[cpr_motor]] steps per turn of its shaft, and the turret turns [[ratio_t]]× slower:

\[ [[cpr_motor]] \times [[ratio_t]] = [[counts]]\ \text{counts per turret turn} \;\Rightarrow\; \frac{360^\circ}{[[counts]]} = [[deg_count]]^\circ\ \text{per count} \]

How precise does it need to be? The opening is 20 in wide, so a Pollen's center can be up to [[half_w]] cm off-center and still fit. From 2.5 m away that's \( \arctan([[half_w_m]]/2.5) = \pm[[aim_deg]]^\circ \). That uses the opening's widest point, so it's a best case. Near the peaked top, the opening is narrower.

What it means: the encoder is far finer than needed. The real limits on aim are gear backlash (the small wiggle room between gear teeth) and knowing exactly where the robot is on the field.

8 · Belt length: finding the center distance

Belts only come in stock lengths. How far apart must the pulleys be for one to fit?

Take two pulleys with pitch diameters \( D_1, D_2 \) (the circle where the belt's teeth sit), with centers \( C \) apart. The belt length is:

\[ L = 2C + \frac{\pi\,(D_1 + D_2)}{2} + \frac{(D_2 - D_1)^2}{4C} \]

HTD 5 mm belts have a tooth every 5 mm, so a pulley's pitch circle has a diameter of \( D = N \times 5\ \text{mm} / \pi \): \( D_1 = [[d1]] \) mm and \( D_2 = [[d2]] \) mm. The design picks the stock [[belt]] mm belt and works out \( C = [[C]] \) mm. Check it:

\[ L = 2([[C]]) + \frac{\pi([[d1]] + [[d2]])}{2} + \frac{([[d2]] - [[d1]])^2}{4([[C]])} = [[L_calc]]\ \text{mm} \]

What it means: the motor mount's middle position is cut at exactly that distance. The adapter slides ±2 mm, which changes the center distance by about ±1.4 mm, so you can set the belt tension on the robot. The jackshaft belt uses the same formula (24T to 24T, 410 mm belt, \( C = 145.00 \) mm) but it can't slide. That's why its test plate matters.

9 · The cable loop's rolling fold

If the cables cross the joint in a rolling loop (one of the options), how far does the U-shaped fold move around its channel when the turret turns?

The ribbon lies along the drum (radius \( r_\text{in} = [[rin]] \) mm), folds, and comes back along the fixed wall (\( r_\text{out} = [[rout]] \) mm; example sizes for a channel around the turret). It never slides, so its length stays the same. An arc's length is radius × angle (in radians), so:

\[ L = r_\text{in}(\theta_U - \theta_\text{in}) + \pi r_b + r_\text{out}(\theta_U - \theta_\text{out}) \]

\( \theta_\text{out} \) is fixed, and \( \theta_\text{in} \) turns with the turret. (\( \theta_U \) is where the fold is, and \( r_b \) is the fold's radius.) Since \( L \) doesn't change, its derivative (rate of change) is zero. That gives:

\[ \frac{d\theta_U}{d\theta_\text{in}} = \frac{r_\text{in}}{r_\text{in} + r_\text{out}} = \frac{[[rin]]}{[[rin]] + [[rout]]} = [[u_ratio]] \]

What it means: the fold moves at [[u_ratio]] of the turret's speed, like a gear rolling between two others. Swinging the turret ±[[travel]]° moves the fold only [[u_travel]]° in total. So it never reaches either end of the [[cable_len]] mm ribbon.

10 · The height budget

How much room is left under the turret for the drivetrain, intake and indexer?

\[ \underbrace{[[lim]]}_{18''\ \text{start cube}} - \underbrace{[[margin]]}_{\text{margin}} - \underbrace{[[start_top]]}_{\text{turret, hood steep}} = [[base_max]]\ \text{mm} \]

After the start, the robot may be up to 29 in tall ([[match_lim]] mm). With the hood flattened for a long shot, the robot is at most \( [[base_max]] + [[match_top]] = [[robot_match]] \) mm ([[robot_match_in]] in).

What it means: the parts below the turret get [[base_max]] mm. Even the tallest position during the match is still far under the limit.

11 · How deep is a counterbore?

On the ball side of each hood carrier, a button-head screw sits in a counterbore (a round, flat-bottomed recess), so nothing sticks out into the ball's path. How deep is it, and how much wood is left under the head?

The laser can't cut halfway into a sheet. So the counterbore is an 8.2 mm hole cut right through the ball-side layer, and the other layer makes its floor. With 3.0 mm layers, the recess is 3.0 mm deep. An M4 button head (ISO 7380) is 2.2 mm tall:

\[ \text{gap} = 3.0 - 2.2 = 0.8\ \text{mm} \]

The plate is [[plate_t]] mm thick in the model. Take away the 3.0 mm recess, and the whole second layer (about 3 mm of wood) is left under the head.

What it means: the head sits 0.8 mm below the ball-side face, so it can't rub a ball. The head presses on the second layer, whose grain runs across the first, so the load is spread over the wood.

Design decisions

How it works

1 · Motor → main shaft (3:1)

2 · Main shaft → jackshaft (1:1)

3 · Jackshaft → upper wheel (60:48)

4 · Squeeze force and the arm stop

5 · Straight-through pinch

6 · Hood angle

7 · Cables across the turning joint

8 · Rear ball guard

Parts list

Print settings for the real parts

Same settings on both printers

Filament settings

Settings by part type

Shaft stacks

Assembly order and adjustments

Shooting at the HIVE from anywhere

What the indexer must do

Check before cutting

Fit tests: do these first

What it costs

Printed prototype

Print settings

Filament and printers

Settings by part type

What to print, step by step

What students can learn from this turret

Physics of the shot

Mechanisms

Structures and materials

Designing for making and fixing

The engineering process

Mechanical ideas in this turret

Keep drives steady while things move

Passing power along

Forces, moments and reactions

Stops, limits and adjustments

Bearings, shafts and fits

Fasteners

The engineering math