// multi-utility computation suite · offline · instant · precise
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eng.robot-dynamics-torque Calculator
Calculates robot joint torques from the dynamic equations of motion including gravity, inertia, Coriolis, and centrifugal terms. Dynamic torques during acceleration are often larger than static gravity torques — servo motor sizing must account for the full dynamic load.
Inputs
M Link Kg
Total mass (kg). Distinct from weight — weight = mass × gravity. Mass is constant; weight varies with location.
L M
Linear measurement. Ensure consistent units: 1 m = 1,000 mm = 3.281 ft.
Theta Dot Rad S
How fast something rotates (rad/s). One full revolution = 2π radians. Convert from RPM: multiply by 2π/60.
Theta Ddot Rad S2
Rate of velocity change (m/s²). Earth's gravity: 9.81 m/s². Objects in free fall accelerate at this rate.
Results
required joint torque τ (N·m)
Rotational force (N·m) = force × perpendicular lever arm. High torque at low RPM is ideal for hauling; high RPM suits high-speed applications.
inertia torque τ_I (N·m)
Rotational force (N·m) = force × perpendicular lever arm. High torque at low RPM is ideal for hauling; high RPM suits high-speed applications.
gravity torque τ_g (N·m)
Rotational force (N·m) = force × perpendicular lever arm. High torque at low RPM is ideal for hauling; high RPM suits high-speed applications.
moment of inertia I (kg·m²)
Sample size or count used in the calculation.
Euler-Lagrange: τ = I·θ̈ + m·g·L/2
The difference between the maximum and minimum values.
motor sizing (2× safety factor)
A dimensionless multiplier applied in the calculation.