This may not apply to the model in question, but a real rocking chair's rails will be not be arcs of a circle;  to prevent falling over, they are hyperbolic arcs (cam profile) - more curved at the center, flatter near the ends.

     The animated origin idea will still work, but it won't quite be a straight line.  You might also experiment with the origin fixed but keyframe the motion sequence repeatedly using drop to floor (I think you'd need to make the chair a figure?), or key several strategically chosen frames manually and let spline interpolation do the rest.

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