described around the center 9 o to form a circle h 2 a tangent with respect to this circle h 2 is described from b 2 and the tangent is extended to a length equal to that of line b 1 d 1 to obtain d 2 similarly d 3 corresponds to b 3 and d 4 corresponding to b 4 are found and if d 1 d 2 and d 3 d 4 are connected respectively by approximate arcs arc segments d 1 d 2 and d 3 d 4 are obtained as will be apparent from comparison between d 1 d 2 and d 3 d 4 in fig4 arc segment d 3 d 4 is substantially the same as arc segment d 1 d 2 and thus when compared with the case in fig2 d 3 d 4 and d 1 d 2 are substantially maintained at a constant the difference between the segment of arc d 1 d 2 and segment of arc d 3 d 4 can further be affected in point of design by the center of curvature and radius of arc c the length of link 5 the position of b 1 positions of roller 9 and pin 3 etc in each case the described operating principle diagram is constructed by finding the relative position of roller 9 with respect to arcuate groove 11 at an arbitrary point during the arcuate movement of pin b and finding how the center line b d of backrest frame 2 in the corresponding position changes its radius with respect to the center 9 o of roller 9 in the diagram reference characters e 3 e 4 perpendicular lines f 3 f.