AuthorCarlo Tuzi
Emailcarlo.tuzi@gmail.com
Date
RevisionRev. 4
Modern Robotics · Chapter 3 · Rigid-body motions

Torque in Two Frames

A box carries its own body frame {b}. Pose it, move it along a screw axis, push on it, and watch every quantity of chapter 3 update in the space frame {s} and the body frame: rotation matrices, angular velocities, exponential coordinates, homogeneous transformations, twists, screw axes and wrenches. Notation follows Modern Robotics (Lynch & Park): [x] is the skew-symmetric matrix of x, and [𝒱] the 4×4 matrix of a twist.

Space viewcamera fixed to {s} · the body moves
Body viewcamera rides with {b} · the world moves
x y z force f moment m (½ scale) screw axis, ω linear velocities position vectors
Try this

Drag inside either view to orbit, scroll to zoom. Pick an experiment above, or start from “Everything to zero” and raise one value at a time.

3.1Rigid-body motions in the plane

3.2Rotations and angular velocities

3.3Rigid-body motions and twists

3.4Wrenches