as best shown in fig1 and 2 , a first hub 11 , is connected to a shaft 12 , such that hub 11 rotates with shaft 12 . any means may be utilized to connect hub 11 to shaft 12 . two outer disks 13 and 14 are rigidly attached to the first hub 11 and are made to be concentric with and perpendicular to shaft 12 and hub 11 . these disks have spiral grooves , or slots , 15 which start on the inside at a convenient diameter and end at their outermost points near the circumference of the disks . the disks 13 and 14 are spaced from each other in a direction along the axis of shaft 12 , as best seen in fig2 . a second hub 16 is disposed between the disks 13 and 14 , about hub 11 . hub 16 has a bearing surface 17 sliding on the outer surface of hub 11 , making the second hub 16 free to rotate with respect to first hub 11 , and shaft 12 . two inner disks 18 and 19 are affixed to hub 16 so as to be adjacent the disks 13 and 14 , and to rotate with hub 16 . disks 18 and 19 have radial slots 20 in the same number and circumferential spacing as the spiral slots 15 in the disks 13 and 14 . chain engaging segments 21 , shown in fig3 - 5 , are provided in the number that there are grooves or slots in each disk . these are disposed between the disks 18 and 19 . the segments have first projections 22 , on each side of the proper size and shape to slidingly engage the radial slots in disks 18 and 19 and sufficient length to reach thru each of the disks 18 and 19 . the segments are not able to turn in said slots because of their flattened contour . second projections 23 , preferably round , project from the first projections and are of a size and length to engage the spiral slots in the disks 13 and 14 . the projections on each segment engage the grooves in both sets of disks ( 13 , 14 ; 18 , 19 ) and , therefore , can have only one radial position for each of the possible angular relations between the two sets of disks . the curves of the spiral grooves 15 are coordinated so that all of the segments 21 are at the same radial distance from the center for each angular setting of the disks . spring 24 , shown in fig1 is connected , between the outer disks ( 13 , 14 ) and the inner disks ( 18 , 19 ), so as to bias them at one extremity of their angular positions , which is limited by the intersections of the spiral slots 15 and radial slots 20 . one possible arrangement is to connect spring 24 around the rim of the disks between anchor 25 attached to one of the outer disks 13 or 14 and anchor 26 attached to one of the inner disks , 18 or 19 . a variable sprocket which is to be used as the driving sprocket is made so that the spring 24 holds the device such that the segments are at their maximum diameter position when no torque is being applied . the torque transmission ratio will be at its highest in this position . when torque is applied to the shaft 12 , it is resisted by the remainder of the drive train ; a point is reached when the spring 24 begins to yield and allow the outer disks 13 and 14 to rotate relative to inner disks 18 and 19 . then the sprocket segments 21 , and the inner disks 18 and 19 with radial slots 20 , will lag behind the driven assembly , consisting of shaft 12 , inner hub 11 and outer disks 13 and 14 , due to the elasticity in the spring 24 . the segments 21 will move inward in unison as the intersection of the radial and spiral grooves move in , due to changing angular displacement between the inner and outer disk assemblies . thus , the torque transmission ratio will be lowered accordingly . application of additional torque will , in the same manner , lower the ratio until the maximum low is reached : in that position the drive sprocket segments are at their minimum diameter and the driving force has its maximum advantage in pulling the load . a variable sprocket which is to be used as a driven sprocket , is made so that the spring 24 holds the device so that the segments are at their minimum diameter positions when no torque is being applied . as a torque load , transmitted by the chain increases above that which the spring 24 can restrain without yielding , the outer disks 13 and 14 , with the spiral grooves , will rotate with respect to and will lag behind the driven inner disks 18 and 19 . this relative angular displacement forces segments 23 to slide up the spiral grooves , and , accordingly , the diameter of the sprocket increases . thus the transmission ratio is lowered and the advantage of the driving force is improved . the change in the torque transmission ratio , associated with a given change in applied torque , can be adjusted by the spring 24 so that the input torque at the driving sprocket will remain with a narrow band of change , as the load on the output shaft changes the full range of ratios available . this is possible because , as the ratios change , the advantage given to the driving force is applied ahead of the point where the force affects the change ( the variable rim of the output sprocket ) and the advantage is effective at this point . thus the additional effort to shift the spring can be offset by the very change in ratio that it caused . too much feedback , of course , will cause the device to shift all the way , without the advantage of gradual change . the gain in advantage , of course , is offset by the fact that the drive sprocket has to make more turns to get the work done . an infinitely variable sprocket must have means to keep the chain in mesh , as the circumferential distance between the sprocket teeth varies as the diameter of the sprocket wheel varies , and the openings in the chain cannot fit all the teeth all the time . this is accomplished by having the teeth on each segment biased in a radially outward direction so that when the rollers of the chain engage the top or forward side of the tooth , the tooth is depressed radially inwardly and will pop up again when the chain slips to where it properly meshes . the chain can even slide backwards over the entire sprocket , or individual teeth . this permits the sprocket to change ratios quickly subject to the torque demands of the drive . one example of providing the biased teeth is shown in fig3 - 5 . the tooth 28 is shaped on its concave engagement side so that it engages the roller on the chain in one direction but will tend to slip under the roller in the opposite direction . the tooth is held radially outward by a spring 27 located within segment 21 . the tension of the spring 27 will yield to pressure of the chain so as to move into the segment 21 whenever the chain roller presses on it from the top or from the convex front side . obviously , the tooth 28 may be attached to segment 21 by any means which will allow it to move radially inwardly with respect to the segment . it may be pivotally attached to the segment such that engagement with the chain roller from the top or front side will cause the tooth to pivot with respect to the segment . as the diameter of the sprocket changes , at least one tooth will be in contact with the active surface of the chain and the other teeth can be counted on to yield to the changing space by sliding into proper mesh on their bias . in the driven position , the last tooth to come into play will yield when the diameter is expanding and the one that is nearing to point of disengaging , will be in contact and pulling . the maximum mismatch across all of the teeth will be one tooth , and this space will be divided between at least half the teeth on the sprocket . an eight tooth sprocket will have only about one sixth of a space slip in making engagement when the pulling tooth leaves the point where it no longer can engage . fig6 illustrates one possible use of the torque operated , infinitely variable diameter chain sprocket of the present invention . the sprocket assembly is utilized as an infinitely variable ratio bicycle transmission . the rear axle of the bicycle is analagous to shaft 12 shown in fig1 and 2 . the transmission , shown generally as element 30 , functions as described previously and is constructed as in fig1 and 2 . by varying the torque applied to the chain by the pedals 32 and fixed diameter sprocket 34 , the torque applied to the rear wheel will be automatically varied as discussed previously . spring chain take up means 36 is provided to maintain a constant tension on the chain as the diameter of the variable sprocket varys .