Statics

The branch of mechanics that studies how forces and torques balance on an object at rest or moving at constant velocity.

Statics is the branch of classical mechanics that studies systems with no acceleration, where the equilibrium condition is that the net force and net torque both equal zero: ΣF = 0, ΣM = 0. In robotics, the most-used result is τ = Jᵀ(θ)F: τ is the vector of joint torques, J is the Jacobian matrix (which maps joint velocities to end-effector velocity), θ is the current joint configuration, and F is the wrench — a combined 3D force and 3D torque — that the end effector applies to the outside world. The formula follows from conservation of power (virtual work), and it answers the question, 'to produce this much force at the tip, how much torque should each motor supply?' When the robot must also hold up its own weight, a gravity-compensation torque is added on top. Force control, gravity compensation, and grasp-force analysis all build on statics; once motion speeds up enough that inertial forces can't be ignored, the analysis has to switch to dynamics instead.

ExampleA robot arm's end effector rests motionless against a tabletop and must press down with 10 N of force: first compute the Jacobian J for the current pose, then use τ = Jᵀ F to find the torque each joint must output, and finally add the gravity-compensation torque that offsets the arm's own weight.

Also called

Robot Statics, Static Force Analysis

Related

Wrench · Jacobian Matrix · Gravity Compensation · Principle of Virtual Work · Quasi-Static Assumption · Dynamics

Sources

Statics - Wikipedia
Modern Robotics 5.2: Statics of Open Chains