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Motor Overview

Introduction

Motors are the most essential actuators in a robotic system, responsible for converting electrical energy into mechanical motion. Different motor types offer varying characteristics in torque, speed, precision, and cost. Proper motor selection is a critical step in robot design.

Motor Classification

Classification Decision Tree

graph TD
    A[Motor Selection] --> B{Precise position control needed?}
    B -->|Yes| C{High torque needed?}
    B -->|No| D{Continuous rotation needed?}
    C -->|Yes| E[Servo Motor]
    C -->|No| F{Stepper precision sufficient?}
    F -->|Yes| G[Stepper Motor]
    F -->|No| E
    D -->|Yes| H{High efficiency needed?}
    D -->|No| I[Linear Motor / Voice Coil Motor]
    H -->|Yes| J[Brushless DC Motor BLDC]
    H -->|No| K[Brushed DC Motor]

    style A fill:#f9f,stroke:#333
    style E fill:#bbf,stroke:#333
    style G fill:#bfb,stroke:#333
    style J fill:#fbf,stroke:#333
    style K fill:#ffb,stroke:#333

Major Motor Types

Type Abbreviation Typical Applications Advantages Disadvantages
Brushed DC Motor DC Brushed Small wheeled robots, toys Simple, low cost Brush wear, limited lifespan
Brushless DC Motor BLDC Drones, legged robots High efficiency, long lifespan Requires driver
Stepper Motor Stepper 3D printers, CNC Open-loop precision, holding torque Low-speed vibration, low efficiency
Servo Motor Servo Robotic arms, precision positioning Closed-loop precision, fast response High cost

Basic Electromagnetic Principles

Torque Equation

The torque produced by a motor is proportional to the current:

\[ \tau = K_t \cdot I \]

Where:

  • \(\tau\) — Motor output torque (N·m)
  • \(K_t\) — Torque constant (N·m/A)
  • \(I\) — Armature current (A)

Back-EMF

A rotating motor generates a back electromotive force (Back-EMF):

\[ V_{emf} = K_e \cdot \omega \]

Where:

  • \(V_{emf}\) — Back-EMF (V)
  • \(K_e\) — Back-EMF constant (V·s/rad)
  • \(\omega\) — Angular velocity (rad/s)

Important Relationship

In SI units, the torque constant and back-EMF constant are numerically equal: \(K_t = K_e\). This arises from energy conservation — electrical power equals mechanical power.

Motor Equivalent Circuit

The voltage equation for a DC motor at steady state:

\[ V = I \cdot R + L \frac{dI}{dt} + K_e \cdot \omega \]

At steady state, \(\frac{dI}{dt} = 0\), simplifying to:

\[ V = I \cdot R + K_e \cdot \omega \]

Speed-Torque Curve

The speed-torque curve is one of the most important motor performance diagrams, describing the relationship between speed and torque at a given voltage.

Key Parameters

Parameter Symbol Meaning
No-load speed \(\omega_0\) Maximum speed with no load, \(\omega_0 = V / K_e\)
Stall torque \(\tau_{stall}\) Maximum torque at zero speed, \(\tau_{stall} = K_t \cdot V / R\)
Rated operating point — Typically at the mid-range of the curve, the highest-efficiency region

Linear Relationship

For an ideal DC motor, speed and torque follow a linear relationship:

\[ \omega = \omega_0 \left(1 - \frac{\tau}{\tau_{stall}}\right) \]

Power and Efficiency

Mechanical output power:

\[ P_{mech} = \tau \cdot \omega \]

Maximum power occurs at \(\tau = \tau_{stall}/2\), \(\omega = \omega_0/2\):

\[ P_{max} = \frac{\tau_{stall} \cdot \omega_0}{4} \]

Motor efficiency:

\[ \eta = \frac{P_{mech}}{P_{elec}} = \frac{\tau \cdot \omega}{V \cdot I} \]

Brushed DC Motor (DC Brushed)

Structure

  • Stator: Permanent magnets (small motors) or field coils (large motors)
  • Rotor: Wound coils (armature)
  • Commutator: Mechanical commutation, paired with brushes

Characteristics

  • Simplest control — speed is adjusted by varying voltage; reversing is achieved by swapping polarity
  • Low cost, suitable for beginners and prototyping
  • Brushes cause friction losses and electromagnetic interference
  • Typical lifespan: 1,000–5,000 hours

Brushless DC Motor (BLDC)

Structure

  • Stator: Three-phase windings (fixed)
  • Rotor: Permanent magnets (rotating)
  • Electronic commutation: Requires a drive controller (ESC)

Characteristics

  • No brush wear, long lifespan (>10,000 hours)
  • High efficiency (85–95%)
  • High power density, good heat dissipation (heat is generated in the stator)
  • Requires position sensors (Hall) or sensorless algorithms

See Brushless Motors and FOC for details.

Stepper Motor

Operating Principle

Converts electrical pulses into precise angular displacements; each pulse corresponds to a fixed step angle.

Common Types

Type Step Angle Characteristics
Hybrid stepper 1.8° (200 steps/rev) Most common, balances precision and torque
Permanent magnet stepper 7.5°–15° Low cost, lower torque
Variable reluctance stepper Depends on tooth count Good high-speed performance

Drive Modes

  • Full stepping: One step per excitation
  • Half stepping: Between two steps, doubling the resolution
  • Microstepping: Sinusoidal current modulation, up to 1/256 step, smoother motion

Limitations

  • Open-loop control — lost steps cannot be detected
  • Prone to resonance vibration at low speeds
  • Torque drops sharply at high speeds
  • Always draws rated current (holding torque), resulting in low efficiency

Servo Motor

System Components

A servo motor is a complete closed-loop control system:

  1. Motor body: Typically BLDC or AC induction motor
  2. Encoder: High-resolution position feedback
  3. Driver: Current loop + velocity loop + position loop
  4. Control interface: Pulse, analog, or bus-based

Control Loop

Position command → [Position Loop] → [Velocity Loop] → [Current Loop] → Motor
                       ↑                  ↑                 ↑
                    Encoder          Encoder diff       Current sensor

Industrial Servo vs. Hobby Servo

Feature Industrial Servo Hobby Servo
Control method Multi-loop closed-loop Built-in PID position loop
Feedback High-precision encoder Potentiometer
Communication EtherCAT/CAN PWM pulse
Price Thousands to tens of thousands of RMB Tens to hundreds of RMB

See Servos and Bus Servos for details.

Robot Motor Selection Guide

Selection Process

  1. Define requirements: Load torque, motion speed, precision requirements, control method
  2. Calculate load: \(\tau_{load} = J \cdot \alpha + \tau_{friction} + \tau_{gravity}\)
  3. Safety margin: Typically select a rated torque 1.5–2 times the load torque
  4. Match gear reducer: Choose a gear ratio based on speed/torque requirements
  5. Verify thermal characteristics: Ensure continuous operation does not exceed motor temperature limits

Typical Application Scenarios

Application Recommended Motor Type Example
Differential drive car Brushed DC + encoder JGA25-370
Multirotor drone BLDC outrunner T-Motor U8
Robotic arm joint Servo / BLDC + reducer Dynamixel XM430
Legged robot BLDC + QDD Unitree Go2 motor
3D printer head Stepper motor NEMA17
Small control surface PWM servo SG90 / MG996R

Key Performance Metrics

\[ \text{Power density} = \frac{P_{rated}}{m_{motor}} \quad (\text{W/kg}) \]
\[ \text{Torque density} = \frac{\tau_{rated}}{m_{motor}} \quad (\text{N·m/kg}) \]

Summary

  • Motors are the "muscles" of a robot; selection directly impacts system performance
  • The torque equation \(\tau = K_t I\) and back-EMF \(V_{emf} = K_e \omega\) are the most fundamental relationships
  • The speed-torque curve defines the motor's operating range
  • Different motor types are suited to different scenarios — there is no universal solution
  • In practical systems, motors are commonly paired with gear reducers, encoders, and drivers

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