In this conveyor belt configuration, rollers P and R are horizontally aligned, while rollers R and S are vertically aligned, in a triangular arrangement. Roller Q then bends the belt between P and S. Roller Q is free to slide vertically, while roller P slides horizontally. The remaining rollers R and S are fixed to their position. Of course all the rollers rotate with zero friction to allow the belt to move. The system is in static equilibrium, held together by an applied horizontal force Fp at P and vertical force Fq at Q. If I know all dimensions and geometrical relationships (angles, distances), how would I relate the belt tension T, and the external forces Fp & Fq?
Off the cuff, it looks like you've done most of the work in that excellent image. Each idler is in equilibrium. The vertical components of the tension forces at idler Q will be equal and opposite to Fq. Ditto for idler P, except horizontal.
