Ignore me.  My morning coffee hasn't taken effect yet.  I now realize that you said that you had made the chair (hence, the rails are arcs of a circle).  Your idea of placing the origin at the center of the radius (not on the floor) will work;  X-translate the chair back and forth, and Z-rotate it simultaneously.  With keyframes at neutral position, both extremes, and a few 'tweens,  the spline interpolation should work nicely.

Poser 12, in feet.  

OSes:  Win7Prox64, Win7Ultx64

Silo Pro 2.5.6 64bit, Vue Infinite 2014.7, Genetica 4.0 Studio, UV Mapper Pro, UV Layout Pro, PhotoImpact X3, GIF Animator 5