What gear ratio should I use to make my arm stronger?

To make an arm stronger, you should increase its gear ratio, which is referred to as gearing down . A higher gear ratio will increase the torque of the arm at the expense of speed . Arms require a high gear ratio and must be well-supported to handle the torque provided by the motor . It is recommended to transfer torque to the arm through a gear, chain, or belt rather than directly mounting to a motor shaft to achieve a larger reduction .

For high-load applications like arms, planetary gearboxes are recommended over spur gearboxes . Spur gearboxes are easily damaged by shock load because only a few teeth from each gear are engaged and carry the entire load .

The gear ratio can also be adjusted by changing the spool size in a linear slide system, where a smaller spool can increase torque . However, this method is described in the context of linear slides, not arms .

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Design Tradeoffs > Single/multi axis arm Linear extension

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Important: Teams are generally advised to stay away from arms and move in the direction of linear slides, primarily due to the issue of complexity. This is because arms typically are less effective than linear extensions and are harder to implement properly.

Arms require a high gear ratio, so arms must be supported extremely well to bear the torque that the motor provides. A poorly supported and/or constructed arm will cause the driver needless pain as it is exceedingly difficult to line up an arm that constantly shakes. In contrast, linear extensions do not need to worry about gear ratios and gearboxes. They can be optimized to be more efficient than arms, and typically are more precise, as linear motion is easier to control than angular motion. Another positive is that linear slides can have more extension than arms, with some reaching 5+ feet in length.

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Kinematics > Manipulators

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Often in FTC, teams have arms that swing out around an axis. Controlling these arms requires a bit of thought as depending on the angle they're at, the effect of gravity drastically changes.

Our first step is defining a reference frame. Our recommendation is to define zero as straight to the side, as this is when gravity has the greatest effect on your arm. Other reference frames will still work, but the exact trigonometry will change.

(Figure: 11329 I.C.E. Robotics)

In a reference frame like this, the relative force of gravity will be equal to the cos of the angle. This makes sense as when the cos function is evaluated at zero degrees, it returns 1, while at 90 degrees where there is no effect of gravity, it returns 0.

Fg = gcosθ

Assuming you have an encoder on your arm, you can find theta (the angle of the arm relative to the vertical) using something similar to the following pseudocode.

Note: DEGREE_PER_TICK can be found by taking 360 divided by your encoder resolution all multiplied by your gear ratio. For example, for a 19.2:1 goBILDA Yellow Jacket (https://www.gobilda.com/5203-series-yellow-jacket-planetary-gear-motor-19-2-1-ratio-24mm-length-8mm-rex-shaft-312-rpm-3-3-5v-encoder/), there are 537.7 ticks per revolution, and so frac{360}{537.7} degrees per tick at the gearbox output shaft. If there was a 2:1 gear ratio after that, then the ticks per revolution would instead be frac{360}{2 times 537.7}

current_angle = (TICKS_AT_ZERO - current_tick) * DEGREE_PER_TICK

The typical way to utilize the effect of gravity you just found, is to pass it in as a feedforward parameter to a PID controller. We cover this in gravity-compensated-feedforward.

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Arms

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Arms encompass a large variety of mechanisms. In FTC, they are used to add extension and flexibility to end effectors. Arms are especially powerful when paired with other mechanisms such as linear extension and mini-turrets.

Arms can be a useful tool for extension. Long arms need large reduction ratios to drive. The example in the Single Arm section uses a 254.5:1 reduction. It is recommended to transfer torque to the arm through a gear, chain, or belt rather than directly mounting to a motor shaft due to axial forces and the ability to get a larger reduction. Due to the large amount of momentum these arms can carry, if suddenly stopped they may be able to break a motor's gearbox or even tip your robot over. Software control can help to reduce the load on motor gearboxes (see /docs/software/concepts/control-loops).

Depending on the application and implementation, arms can be either faster or slower than other extension options.

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Rigging > Picking the right spool size

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Spools have a special property that isn't often discussed, but is extremely useful when creating linear slide systems. Just as the system's speed and torque can be changed by changing its gear ratio, speed and torque can also be changed by changing the spool size. The motor rotates the spool at a constant angular speed. Thus, the translational speed (the speed of the slide) is proportional to the radius of the spool, and since torque is inversely proportional to speed, changing the spool size changes torque as well.

This is important to recognize, as changing spool size is often more convenient than changing gear ratio to get the desired combination of speed and torque. To illustrate this, say you have a linear extension system with a 3.7:1 gear ratio. You then decide that a 5:1 gear ratio would provide a more desirable combination of speed and torque than your current 3.7:1 ratio.

In many cases, instead of swapping gearboxes, it makes more sense to swap out spools to a smaller one. If your spool is currently 2 inches, your new size should be frac{2*3.7}{5} inches to achieve the same result.

You also need to make sure that when fully wrapped on the spool, your cable or string doesn't overlap. Overlapping can result in a change in spool diameter, which will change the tension in your string.

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Gearbox Internals

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Fundamentally, a gearbox is just a collection of gears and an enclosure that connects them. Gearboxes have an output ratio, the final Gear Reduction between the motor input and the final output shaft.

Term: Gear Reduction — Also known as a gear ratio. In any rotational power transmission system (typically involving motors and servos in FTC®), a gear ratio defines both the number of rotations of the system's input and the number of rotations of the output.

For instance, a NeveRest 20 gearmotor consists of an unmodified NeveRest Motor and a planetary gearbox that has a gear ratio of 20:1 (or, when spoken, "20 to 1"). This means that in order for the output shaft of the gearbox to rotate 1 time, the input shaft of the motor must rotate 20 times. Gear ratios are one of the most important design considerations about a power transmission component.

Any motor or servo has two properties: speed and torque (or rotational force). These two properties are inversely proportional, meaning that increasing speed decreases torque, and vice versa. For instance, if one wishes to make a mechanism faster at the expense of torque by doubling the speed of that 20:1 gearbox, they would decrease the gear ratio by a factor of 2. Since 20 divided by 2 is 10, the new desired ratio would be 10:1 (this is referred to as gearing up). However, if one wishes to double torque instead, making the system more powerful and robust at the expense of speed, they would increase the gear ratio by a factor of 2, leaving them with a 40:1 ratio (this is referred to as gearing down).

The most common ways of gearing up or down are using gearboxes, gears, sprockets and belt-driven pulleys, all of which exist in various sizes.

In FTC, gearboxes may be more common than you think. Nearly every motor and servo has a gearbox attached or built-in to it. These gearboxes are either spur or planetary.

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Gearbox Internals > Spur Gearboxes

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Term: Spur gearbox — A spur gearbox has spur gears which are stacked on top of each other. Gear reduction is achieved through different size gears on the same plane.

Spur gearboxes are an arrangement of gear ratios, often stacked to achieve a large compound ratio (e.g. 40:1). Each individual ratio only has two gears- one may be 8:1, another may be 5:1, but the final ratio will be 40:1. These gearboxes are used in the AndyMark NeveRest Classic series and goBILDA's 5201 series motors, as well as REV HD Hex Motors. Due to the nature of how these gearboxes are built, each reduction only has a few teeth from each gear engaged, and those teeth carry the entire load of the gearbox. It's easy to damage a spur gearbox from shock load, and if one gear breaks, the entire gearbox will stop functioning.

Tip: Using spur gearboxes on high-load applications such as drivetrains or arms is not recommended. Instead, use planetary gearboxes.

(Figure: Example of a spur gearbox inside a servo. Note how all gears mesh with only one other gear.)

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