Education Lab / Robotics Theory Basics
Torque & Gravity
Torque is the turning effect of a force about an axis. A force creates more torque when its line of action passes farther from the joint. The relevant distance is perpendicular to that line, rather than simply the length of a link.
Why it matters for a robot
A collaborative robot must support its links, wrist and payload against gravity. In the horizontal pose used in our first design study, their gravity torques add at the shoulder. At other poses, the perpendicular distances change.
Core equations
τ = r F sin θ = F d⊥
τg = m g d⊥
τ is torque (N·m); r is the axis-to-force distance (m); F is force (N); θ is the angle between r and F. d⊥ is the perpendicular lever arm (m). For gravity, m is mass (kg) and g ≈ 9.81 m/s2.
A small worked example
Take a 1.0 kg point payload 0.30 m horizontally from a joint. Its downward force is 1.0 × 9.81 = 9.81 N. The perpendicular lever arm is 0.30 m, so τg = 9.81 × 0.30 = 2.94 N·m. This is only the payload contribution; a real arm also includes link and tool weights at their centres of mass.
Measure the lever arm perpendicular to the gravity force.
Common mix-ups
A longer link does not always mean a larger gravity torque: orientation matters. Also, torque uses N·m, but it represents a turning effect rather than energy, even though a joule has the same dimensional units.
Reference: OpenStax · Torque.
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Related concept: Dynamic Torque →