Robotics
Screw theory
Definition
Screw theory is a geometric framework for describing rigid-body motion and forces using axes, rotation, translation, and pitch. In robotics it provides the basis for twist and wrench representations and screw-axis formulations of kinematics.
Updated
Rotation and translation share an axis
A screw motion combines rotation about an axis with translation along it. Pitch relates the translation to the rotation. Zero pitch gives pure rotation; pure translation is treated as a limiting case with no angular component.
Modern Robotics shows how an instantaneous rigid-body velocity can be represented by a screw axis and a scalar speed. The resulting six-component velocity is a twist.
From joint axes to robot motion
A revolute joint contributes rotation about its joint axis. A prismatic joint contributes translation. Their screw-axis descriptions allow a common mathematical treatment even when a chain mixes joint types.
The product-of-exponentials formulation composes these joint motions to calculate forward kinematics. The corresponding finite motion comes from integrating a constant twist, as explained in the exponential-coordinates lesson.
Geometry is not a drive mechanism
The word “screw” describes a geometric motion, not a requirement for a threaded mechanical screw. The framework also packages forces and moments as wrenches, described in the force-representation lesson. It describes ideal rigid motion and force relationships; deformation and actuator dynamics require additional models.
Sources
Related terms
Twist
A twist is a six-component representation of a rigid body's instantaneous motion, combining angular and linear velocity. Its numerical values depend on the reference frame and the point used for the linear component.
Wrench
A wrench is a six-component representation of force and moment acting on a rigid body. It combines three force components with three moment components about a specified reference point.
Forward kinematics
Forward kinematics calculates the position and orientation of a robot link or end-effector from the robot geometry and joint positions. It maps a robot configuration to a pose.