Introduction

VEX Robotics DC Motor Introduction

Motion is an integral part of mobile robotics. Whether robots are lifting an object, spinning a wheel, or performing some other action, they almost always include some form of actuator. The most common way to achieve such motion is through the use of a motor, and the most common type of motor used in hobbyist or competition robotics is the direct current (“DC”) motor.

DC motors, at their core, operate under a straightforward principle: the conversion of electrical energy (an input voltage and drawn current) into mechanical energy (an output shaft spinning at some speed, with some amount of torque).

The amount of mechanical output produced by a motor is dependent upon the amount of load placed upon it. This concept is key to understanding DC motor performance. As load (or mechanical resistance) increases, motors will draw more current and output more torque to overcome this load. However, as that torque increases, speed decreases proportionally. Additionally, as current draw increases, battery life decreases and wear on the motor increases.

To learn more about the relationships between speed, torque, and power, visit Unit F.4 of the VEX IQ Curriculum or Unit 7.2 of the VEX EDR Curriculum.

For a more in-depth look at DC motors and their use in robotics, visit Unit 7.3 of the VEX EDR Curriculum.


The Four Key Characteristics of DC Motors (top)

These tradeoffs must all be considered when designing a mechanism that uses a motor in a particular application. To help understand a specific motor’s capabilities in such an application, four key characteristics are used to define a motor’s performance:

  • Free Speed (RPM) – The maximum speed at which a motor will rotate when under no load
  • Free Current (A) – The minimum current a motor will draw when under no load
  • Stall Torque (N ∙ m) – The amount of load placed on a motor that will cause it to stall (stop moving)
  • Stall Current (A) – The amount of current drawn by a motor when it is stalled

These characteristics represent the theoretical minimum and maximum conditions for a motor. Under no load, a motor spins at its Free Speed and draws a Free Current. Conversely, Stall Torque and Stall Current represent a motor being worked to its maximum, to the point at which it can no longer move.

In good mechanism design, motors rarely operate at one of these four edge conditions. Holding something at stall torque (with max input voltage) is a great way to quickly destroy a motor, and spinning at free speed ensures that very little actual work can be done (since max speed corresponds to zero torque). Instead, engineers use motor curves to optimize motor usage somewhere in the middle.

The "Down-Up" Dyno Test (top)

VEX Robotics motor curves were developed experimentally using a “down-up” dynamometer test.

1. A motor is spun at free speed
2. A brake is slowly applied (linearly increasing in torque over time), bringing the motor down to a predetermined RPM
3. The brake is slowly released and the motor is allowed to return to its free speed

A variety of data, such as output speed, output torque, current draw, and power input/output, is taken throughout this test. The “down” (brake applied) side is then averaged with the “up” (brake released) side.

Why "Down-Up"?

The mechanics of a dyno test are crucial to developing and publishing accurate motor specifications. When a motor is spinning at free speed while attached to a dyno drum, the system contains a high amount of rotational inertia. This inertia complements the motor’s own output, creating a false reading for peak output power that can be higher than the motor’s actual performance.

However, manufacturers do not always adjust for inertia cancellation when measuring their motor’s performance, and spec sheets rarely detail the circumstances under which their information was derived.

By testing and averaging both the “down” (inertia helping the motor) and “up” (inertia resisting the motor) sides, this method is the best way to represent a motor’s true capacity.


Using a Motor Curve (top)

Motor curves are primarily used in two scenarios: Determining what motor (and gear reduction) to use in a particular application, and learning more about the state of a motor currently operating in a system.

1 - Determining which motor (and gear reduction) to use in a particular application

"Which motor should I use to lift this object?"


In competition robotics, the task to be performed will need to be defined and modeled by the designer. As a simplified example, consider a game piece that weighs 40.0 N, being lifted by an arm that is 0.5 m long, running through a 100:1 gearbox:

Thus, the motor that drives this arm will need to output 0.2 N · m of torque.
Note: To learn more about how gear ratio can affect speed and torque, visit Unit G.3 of the VEX IQ Curriculum or Unit 8.4 of the VEX EDR Curriculum.

This output torque requirement can then be compared against published Motor Curves to learn more about the state of the motor during this action. Consider the following two curves [click to enlarge]:

Motor A achieves 0.2 N · m of torque at roughly 13000 RPM, drawing roughly 40 A.
With a 100:1 gearbox, this equates to an arm speed of 130 RPM.
At this torque, the motor is operating just under 60% efficiency, below its peak.

Motor B can achieve 0.2 N · m of torque at roughly 5000 RPM, drawing roughly 20 A.
With a 100:1 gearbox, this equates to an arm speed of 50 RPM.
At this torque, the motor is operating at around 60% efficiency, very near its peak.

Using these types of calculations, an engineer can combine this information with other details of the system to determine the best motor for their application. Is 50 RPM too slow? Is 40 A too high of a current draw? Is a higher efficiency needed for thermal or battery reasons?

As should quickly become evident, there are a number of variables involved in making this determination. Gear ratio, arm length, even game piece weight. Many times, designers will develop spreadsheet calculators to modify these values and seek out a condition that satisfies their needs.

Note: Current Draw at Peak Power

For an even quicker "back of the napkin" calculation, designers will sometimes simply calculate the amount of work being performed (Work = Mass × Gravity × Height) over a set amount of time (Power = Work ÷ Time) and select a motor matching that power requirement. For example, if a robot had to lift a 20.0 kg object 1.0 m in the air over 1.0 second:

In the above example, Motor B would be the closest match for a power requirement of 196 W.

However, what happens when there are two motors matching that peak power need? It is generally best to choose the motor with the lowest current draw, as this will extend your battery life and reduce strain on the electrical system. This becomes especially important under a sustained load, when current limiters or circuit breakers must be taken into account. This is covered in more detail below.

2 – Learning more about the state of a motor currently operating in a system

"Why does this motor burn up after lifting the object?”


If a motor has already been installed and an engineer wants to know more about the state of the system, the same theory as above can be reversed. At a known voltage, it takes one measured value (such as current draw) to determine the rest of the motor’s attributes at that moment.

For example, again consider Motor A. If an ammeter is used to measure a current draw of 25 A, then it is now known that the motor is exerting around 0.11 N · m of torque and is operating around its peak efficiency of just under 70%. However, if the ammeter is reading 140 A, then the motor is currently operating under an extreme stall condition.

Note: VEX Robotics motor curves were made at 12 V. The four key characteristics (free speed / current, stall torque / current) approximately scale proportionally with system voltage. If Motor A was running at 6 V, its stall current would drop from 130 A to 65 A, and its stall torque would drop from 0.7 N · m to 0.35 N · m. If an ammeter reading showed a current draw of 25 A:


Other Considerations (top)

While motor curves are an immensely useful tool to use during mechanism design, there are a few other characteristics of a motor or a system to keep in mind.

Thermal Mass

Most motors, if pushed to their stall torque or peak power, will burn themselves out if left there for too long. However, that acceptable time varies from motor to motor. Some motors may have a very high peak power, but can only be run under that full power in short bursts. Other motors have no problem sitting at their peak power, but may have other drawbacks (higher current draw, lower peak power, etc).

Because this property is so inherently dependent on the system and application, it is not typically published by manufacturers. However, thermal mass can be approximated by dividing a motor’s peak power by its weight. For example:

  Peak Power Motor Weight Thermal Mass
Motor A 330 W 0.75 lb 440 W/lb
Motor B 215 W 2.16 lb 99.5 W/lb

In this scenario, Motor A would be more useful for shorter bursts of high power, while Motor B could sustain its power for much longer. However, this comparison should only be used as a relative approximation, not as a firmly defined property.


Current Limits

Most competitive robots involve some sort of safety cutoff, such as a thermal cutoff inside the motor or a current limiting circuit breaker. These limits must be taken into account when determining an acceptable current draw for a given application.

Circuit breakers can usually hold a current draw past their rating for a set amount of time. Manufacturers typically provide a spec sheet that includes a graph such as the following, taken from the 20A / 30A Snap Action VB3 circuit breakers sold by VEXpro:

If Motor A from the above example (drawing 40 A) were wired through a 20A breaker, it would be pulling 200% of the breaker’s rated current. Referencing this chart, the system could sustain this draw for roughly 1 – 4 seconds before tripping the breaker and cutting power to the motor.

Mathematical Assumptions

Though the motor curves are experimentally built, the calculations they are being used for ignore many real-world system characteristics such as friction, shock loading, or the effects of gravity (such as when moving an arm up vs moving it down). In some cases, these assumptions lend themselves to a more conservative calculation; in some cases, the opposite is true.

It is important to remember that the engineering design process consists of much more than calculations based off of spec sheets and charts – once a direction has been set, it’s time to build a prototype, test, and iterate as required!