Search Results

15 results for “robotics”

Formulae (15)

u(t) = K_p e + K_i \!\int e\,dt + K_d \frac{de}{dt}

Control output from proportional, integral and derivative of the error.

DoF = 6n - \sum c

Independent motions of a mechanism from bodies and constraints.

\tau_{out} = \tau_{in} \times GR \times \eta

Output torque after gear reduction, allowing for efficiency.

\theta = \frac{360}{N}

Smallest angle a rotary encoder can resolve.

\tau = k_t I

Torque of a DC motor is proportional to current.

V_b = k_e \omega

Voltage a spinning motor generates against its supply.

x = L_1\cos\theta_1 + L_2\cos(\theta_1+\theta_2)

End-effector position from joint angles of a two-link arm.

\tau = I\alpha

Torque needed to angularly accelerate a rotating mass.

\theta = \frac{360}{S}

Angle turned per step from steps per revolution.

\theta_m = \frac{\theta}{m}

Finer step angle from microstepping a stepper motor.

d = 2\pi r \frac{C}{N}

Distance a wheeled robot travels from encoder counts.

t_s \approx \frac{4}{\zeta \omega_n}

Time for a control response to settle within 2% of target.

f = \frac{1}{T}

Frequency of a control loop from its cycle time.

\tau = m g L

Torque a joint must hold to support a payload at reach L.

t = \frac{Q}{I}

Runtime from battery charge and current draw.