On Plane-Symmetric Rigid-Body Motions

This work studies the neglected subject of plane symmetric rigid-body motions. A plane symmetric motion is generated by reflecting a rigid body in successive planes of a one parameter family of planes. To make this a rigid-body motion we begin by reflecting the body in a fixed initial plane before reflecting in the next plane of the family. In particular the twist velocity and fixed axodes of these motion are investigated. Three families of planes can be associated to a space curve, the osculating, normal and rectifying planes. The plane symmetric motions generated by each of these families is investigated. The acceleration centre of the general plane symmetric motion is found together with some other properties of the acceleration of this motion. Special curves are known that have partner curves, the relationship between motions defined by some of these curves and their partners is studied. Finally, line symmetric motions generated by the normal and binormal lines to a curve are studied as combinations of pairs of plane symmetric motions