fig1 is a composite front elevation of a bicycle seat , left side showing the transverse beam adjusted to the maximum length , and right side showing the transverse beam adjusted to the minimum length . fig2 is a horizontal section through the transverse beam and seats . fig3 is a vertical section through the transverse beam and the central ball and socket joint and the seat mount bearings . fig4 is a vertical section 90 degrees across the centerline of the transverse beam through the central ball and socket joint . fig5 is a vertical section 90 degrees across the centerline of the transverse beam through the seat mount bearings . fig6 is a horizontal section through the upper part of the transverse beam . fig7 is a plan view of a portion of the seat support . fig8 is a side elevation of a portion of the seat support . fig9 is a front elevation of a portion of the seat support . fig1 is a plan view of a portion of the seat support . fig1 is a side elevation of a portion of the seat support . fig1 is a front elevation of a portion of the seat support . fig1 is a plan view of a portion of the seat support . fig1 is an elevation of a portion of the seat support . fig1 is a plan of a portion of the seat support . fig1 is a plan of a portion of the seat support . fig1 is an elevation of a portion of the seat support . fig1 is a plan view of a bicycle with the seat installed . fig1 is a side elevation of a bicycle with the seat installed . fig2 is a rear elevation of a bicycle with the seat installed . fig2 is a side elevation of a pelvic bone and buttock seated on the seat as it would appear with the near pedal at 2 o &# 39 ; clock position . fig2 is a rear elevation of a pelvic bone and buttocks seated on the seat as it would appear with the right side pedal at 2 o &# 39 ; clock position . fig2 is a plan view of a pelvic bone seated on the seat as it would appear with the right side pedal at 2 o &# 39 ; clock position . arrows drawn through the femur sockets of the pelvic bones show how these axes gyrate in sympathy with and remain parallel to the transverse beam of the seat . fig2 is a matrix of views of the bicycle seat at four different pedal positions as a means of illustrating how the seat articulates its way through a pedaling cycle . the four positions are identified ( from top to bottom ) as the angle of the pedal crank arms as compared to the identical angles of the hour hand of a clock . starting from the top and proceeding toward the bottom in the first column , the angles taken as examples of pedal positions are as at 2 o &# 39 ; clock , 5 o &# 39 ; clock , 8 o &# 39 ; clock , and 11 o &# 39 ; clock . the seat is illustrated from left to right on the page as a right side view , a rear view , and a top view . the matrix of views is formed as each pedal angle is illustrated in each view . throughout the pedaling cycle , in every case , a line drawn through the sockets of the pelvis which hold the upper ends of the femurs will remain parallel to the transverse beam of the seat . thus the seat allows the pelvis to move freely without constraint as it would in running . fig2 is a horizontal section through transversely perforated block and assembled transverse beam shown at maximum and minimum extensions . fig2 is a front elevation of the bicycle seat with the transverse beam shown at maximum and minimum extensions . fig2 is a side elevation vertical section through the transversely perforated block and the assembled transverse beam . fig2 is a front elevation of a portion of the seat support . fig2 is a plan of a portion of the seat support . fig3 is a side elevation of a portion of the seat support . fig3 is a front elevation of a portion of the seat support . fig3 is a side elevation of a portion of the seat support . fig3 is a plan of a portion of the seat support . fig3 is a plan of a portion of the seat support . fig3 is a front elevation of a portion of the seat support . fig3 is a front elevation vertical section through the central bearing showing parts 214 , 216 , 310 , 220 , 224 , 226 . fig3 is a side elevation vertical section through the central bearing and the assembled transverse beam . fig3 is a horizontal section through the lower part of the central bearing . fig3 is a composite front elevation of a bicycle seat , left side , showing a transverse beam adjusted to the maximum length , and right side showing the transverse beam adjusted to the minimum length . fig4 is a front elevation of the right end of the bicycle seat , showing the seat structure tilted toward the transverse beam part 28 , and showing how the seat mount 36 does not contact the transverse beam in this tilted position because of cut out 62 . fig4 is a side elevation of the bicycle seat showing the seat structure in a forward tilted position and showing how the seat mount 36 does not contact the transverse beam part 28 because of cut out 62 . 17 , plan view centerline of rectangular split block 19 219 , shallow holes arranged in circle in short cylinder 216 223 , shallow holes arranged in circle in short cylinder 220 to be good ergonomically , an interface between human and bicycle should allow a close ( e . g ., the closest possible ) approximation of the way the human skeleton is articulated in the act of running naturally . the bicycle seat , as a principle part of the human to bicycle interface , should support part of the rider &# 39 ; s weight , while not interfering unnecessarily ( e . g ., by interfering to the least possible degree ) with the natural articulation characteristic of the running body , and with the flow of blood to and from the rider &# 39 ; s legs and feet , and should create little ( e . g ., the least possible ) friction anywhere in the rider plus bicycle system . here we describe a divided and fully articulated bicycle seat that is ergonomically designed to support the weight of the rider on his two buttocks and not constrain the motion of the rider &# 39 ; s body in any direction except the straight down direction ( in resisting gravity ), and then only proportionally to the way the weight of the rider is distributed between the buttocks at a given instant during each pedaling cycle . there are two separated seat parts , each supporting one of the rider &# 39 ; s buttocks ( we sometimes refer to the seat parts as buttock supports ). each of the seat parts is designed to move and reorient itself freely with the position and orientation of the buttock seated on it , during the pedaling cycle , and not to move at all relative to the buttock , creating no friction between the buttock and the seat part . in some implementations , as the rider pedals , a transverse beam on which the two seat parts are mounted gyrates through three - dimensional space , following and not resisting at any point in the pedaling cycle the natural motion of buttocks attached to legs which are driving pedals . the ball and socket joints through which the seat parts are mounted at two places ( e . g ., at the ends ) of the transverse beam gyrate in sympathy with the beam while a surface of each of the seat parts continually reorients itself to maintain a constant orientation relative to the corresponding buttock . the buttock supporting seat parts of this structure , whose mounts allow them to tilt in any direction and rotate independently from the transverse beam on whose ends they are mounted , maintain constant contact with the lower surfaces of the buttocks and tilt and rotate relative to the transverse beam exactly in sympathy with the buttocks throughout the pedaling cycle , and thus do not rub against them . therefore no ( or as little as possible ) friction is created between the rider &# 39 ; s skin and this structure . this arrangement of universal ( e . g ., ball and socket ) joints functionally mirrors the arrangement in the human body , in which the pelvic bone is free to gyrate relative to the bottom of the spine , and the femurs are free to gyrate relative to the ends of the pelvic bone . as the free flowing action of the seat does not constrain the body in the act of pedaling ( in other words , the femurs and pelvic bone are completely free to move and gyrate as they normally do while running ), it is also true that it provides the rider &# 39 ; s crotch with no way to stabilize or constrain the bicycle . this however is not needed because the rider can support herself and control the bicycle with the handlebars and by shifting her weight on her hands and feet on the handlebars and pedals . while it is true that riders have traditionally used saddles to create stability and help steer , the loss of this is as nothing compared to the benefit of the freedom of motion and the loss of friction between the rider and the bicycle of the saddle being described here . some implementations are illustrated by example in fig1 ( a front elevation of the assembled parts of the seat ), and fig2 ( a horizontal section through the plan view of the transverse beam and seats ). as shown in fig3 , thin bungee cords of no great strength may be added to the vertical post 14 and to the transverse beam end posts , left side and right side 30 and 32 , to gently return the transverse beam and the seat sections to square and level default positions , when not being pushed by the rider , to facilitate the act of mounting the bicycle . a thin bungee cord 68 passes through holes 66 and 70 in vertical post 14 and transverse beam end posts 30 and 32 , and is fixed in place under light tension by knots 72 , typical . two other bungee cords 76 pass through holes 74 and 78 in transverse beam end posts 30 and 32 and seat mount sockets 34 and 36 and are fixed in place under light tension by knots 80 , typical . the bungee cords may be of thin diameter , ⅛ ″, for example , and under the minimum tension needed to pull the transverse beam and seat mounts to square and level positions . this tension need only be very light as the elements of this structure weigh little and are well balanced on their mounts . a variety of other devices and combinations of them could be used to provide such tension , including curved flat leaf compression springs and coil springs . as also shown in fig8 , in some instances , a seat post shaft 10 is a 14 ″ long ( a ) cylinder of a diameter which fits inside the seat post of the bicycle , and which can be used to adjust the seat height by sliding it into and out of the seat post to the desired height and tightening the bicycle &# 39 ; s own seat post clamp . the seat post shaft 10 may be made of aluminum or steel or glass reinforced plastic ( grp ) or plastic and carbon fiber composite , for example . a short ( for example , about 3 ″ measured from the centerline of the shaft to the centerline of the post ( a 1 )) cantilevered beam 12 of the same material , for example , is welded to , or integrally cast with the seat post shaft 10 at its top end , at an angle of about 115 degrees , such that , with the seat post shaft 10 inserted in the bicycle seat post , the cantilevered beam 12 will be level and extend , cantilevered aft along the centerline of the bicycle , about 3 ″, so that the rider sitting on the seat will have the same relative position ( fore and aft ) to the pedals and handlebars he would have if sitting on a traditional saddle . at its free end the cantilevered beam 12 turns vertical , for example by the same means it previously turned horizontal , to form a short vertical post 14 , for example , 1 ″ from the top of the beam to the bottom of the spherical finial ( a 2 ). at its top end , the vertical post 14 is reduced in diameter to ¾ ″ ( a 3 ) and ends in a 1 ″ diameter ( b ) spherical finial 16 . if the vertical post 14 is made of aluminum or steel tubing , the central joint ball 16 may be made of cast aluminum , or grp , or composite , or nylon , for example , and made as a separate piece and inserted in the end of the vertical post 14 . if the seat post shaft 10 , the cantilevered beam 12 , and the vertical post 14 are made of grp or composite , the central joint ball 16 may be an integral part of the whole casting . the central joint ball 16 acts as the ball of a ball and socket joint which connects the seat post shaft 10 , the cantilevered beam 12 , the vertical post 14 , and the central joint ball 16 , shown assembled in figures land 8 , to the assembled transverse beam . as shown in fig4 , for example , a central socket , forward half 18 and a central socket , aft half 20 are two identical halves of a rectangular nylon block which is split in half along the lengthwise vertical centerline 17 , as also shown in fig1 , 12 , and 13 . the identical parts 18 and 20 each measure , for example , 3 ″ long ( g ), ⅞ ″ wide ( h ), and 1½ ″ high ( i ), so that , when assembled , split block 19 measures 3 ″ long , 1¾ ″ wide ( j ), and 1½ ″ high . the split block halves 18 and 20 are hollowed to form a spherical socket for which the central joint ball 16 forms the ball . a channel 21 ( see fig1 , 12 , and 13 , for example ) is cut in the bottom of the assembled block , lengthwise , of a width to pass the ¾ ″ diameter stem of post 14 , and cut increasingly deeply going from the ends toward the center . this channel will allow the assembled transverse beam to rock from side to side relative to the bicycle , but not to tip forward or aft . this ball and socket joint also allows the assembled transverse beam to rotate on a vertical axis while at any angle of side to side rocking . the two halves of the rectangular split block 18 and 20 have two bolt holes 23 , 25 , ¼ ″ in diameter , passing through the assembled block horizontally through the vertical longitudinal centerline split . the two ¼ ″× 3 ″ hex head bolts with nuts and washers 22 and 24 , which hold all of the parts of the transverse beam together , pass through these holes . the two halves of the rectangular split block 18 and 20 may alternatively be made of aluminum , or grp , or composite , for example . the transverse beam has a left side and a right side 26 and 28 that comprise two identical flat pieces as shown with dimensions in fig9 and 10 . in some implementations , the main flat section is , for example , 5 / 16 ″ thick , 1½ ″ high ( c ), and 4⅜ ″ long ( d ). the adjoined section , which is bent toward the plan view transverse beam centerline 17 , is , for example , 5 / 16 ″ thick ( f ), 1⅜ ″ long , and reduces in height from 1½ ″ at the end joined to the main flat section to 1 ″ height at the end which connects to a ½ ″ diameter ( d 1 ) vertical post with a ¾ ″ diameter ( d 2 ) spherical finial on top with a total height of 2⅛ ″ . the two sides of the transverse beam 26 and 28 bolted together on either side of assembled rectangular split block halves 18 and 20 form the transverse beam which supports and connects the divided seat sections . two rows of evenly spaced ¼ ″ diameter holes 29 arranged respectively along the two sides of the transverse beam 26 and 28 are bored to align with the two holes in the assembled halves of the rectangular split block 18 and 20 , such that pairs of holes in the two sides of the transverse beam 26 and 28 can be selected and aligned symmetrically on either side of the assembled halves of the rectangular split block 18 and 20 , such that the centers of the seat sections 38 and 40 at the ends of the transverse beam are as far apart as the bones of the buttocks , ( ischeal tubularities ), of the particular rider . all of the figures showing the seat assembled show the left side of the transverse beam 26 bolted on in its shortest position and the right side of the transverse beam 28 bolted on in its longest position . in typical use , the two parts would be bolted on symmetrically , so the center of the central joint ball 16 and the longitudinal center of the assembled transverse beam align . the ends of the two sides of the transverse beam 26 and 28 extending beyond the rectangular split block 19 bend toward the plan view longitudinal centerline of the transverse beam such that the centers of the seat sections and the center of the central joint ball 16 align in plan view . the vertical dimension of the two sides of the transverse beam 26 and 28 is reduced as they approach their connections to two ½ ″ diameter ( d 1 ) transverse beam end posts 30 and 32 , to allow clearance for the seat sections to gyrate freely . the left side and right side transverse beam end post 30 and 32 are ½ ″ diameter posts that have corresponding ¾ ″ diameter ( d 2 ) spherical finials on top , as shown in fig9 and 10 , for example . these finials act as the balls for ball and socket joints which connect the respective two seat parts to opposite ends of the transverse beam . the left side and right side transverse beam end posts and balls 30 and 32 may be cast integrally with left and right sides of the transverse beam 26 and 28 , if made of aluminum or grp or composite , for example . left side and right side seat mount sockets 34 and 36 are hollowed nylon blocks , as shown in fig1 and 17 , which act as the sockets which fit on the finials of the transverse beam end posts and balls 30 and 32 . hollowed blocks 34 and 36 are square in plan view and measure 1½ ″ by 1½ ″ ( k ), for example . in side elevation they measure 1 ″ high ( l ), for example . the hollowed blocks may pop on or they may be split and assembled around the balls using fastenings or adhesives . they may be made of aluminum , or grp , or composite , or cast as integral parts of the seat parts 38 and 40 . when mounted on the transverse beam end posts and balls 30 and 32 the hollowed blocks are free to tilt at least about 15 degrees , for example , in any direction from a level position , but the hollow blocks serve as stops to prevent tilting of the two seat parts farther than that permitted amount of tilting . the two seat parts 38 and 40 , shown in fig1 and 15 , for example , are two 4 ″ diameter disks , slightly concave in both horizontal dimensions on top , and are covered by left side and right side seat upholstery 42 and 44 . the upholstery may be cotton batting covered with canvas , or foam covered with plastic , or sheepskin , fuzzy side up , for example . the left side and right side seat mount sockets 34 and 36 are fastened concentrically to the bottom sides of the seat parts 38 and 40 with fastenings or adhesives , or may be cast together with the seat parts 38 and 40 as single units . the seat parts 38 and 40 are made of aluminum , or grp , or composite , or other plastic , for example . fig5 and 41 both show a vertical section 90 degrees across the transverse beam through the seat mounts , showing how the left and right sides of the transverse beam 26 and 28 are cut away 60 , 62 , ( see also fig1 ) at their outer ends to allow clearance for the seat parts and seat mount sockets to gyrate . fig4 shows a side elevation of seat part 40 and seat mount socket 36 in a forward tilted position 64 , and how transverse beam cutout 62 allows clearance in this position . fig4 is a front elevation of the right end of the bicycle seat , the left end being identical , showing the seat structure tilted toward the transverse beam part 28 , and showing how seat mount 36 does not contact the transverse beam in this tilted position because of cut out 62 . fig4 and 41 show the seat mount socket passing as close as it ever comes to the transverse beam in the seat &# 39 ; s three - dimensional gyrating path , thus showing that these parts never come in contact . fig2 shows a horizontal section through the transverse beam assembly with its ball and socket joint , ball 16 , rectangular split block 19 , bolts 22 and 24 , and through the balls 30 and 32 and sockets 34 and 36 joints of the seat mounts , and shows in outline separated seat parts 38 and 40 above the transverse beam assembly . fig2 shows how the elements of the transverse beam are bolted together , and how pairs of holes can be selected from the rows of holes in the left side and right side transverse beams 26 and 28 to align with the two holes in assembled rectangular split block 19 to create a transverse beam of desired length . fig6 shows a horizontal section through the transverse beam near its top . this shows how the forward and aft halves of the central socket 18 and 20 are split on their longitudinal vertical centerline and how the bends in the left side and right side of the transverse beam 26 and 28 make the centers of the left side and right side transverse beam end posts and balls 30 and 32 align with the plan view centerline 17 of the transverse beam . when a human is running , the femur sockets at the right and left ends of the pelvic bone gyrate in a way that causes the pelvic bone &# 39 ; s horizontal axis to outline a horizontally oriented point to point double vortex with the adjoined points coming together at the base of the spine . the femur sockets themselves outline forward rolling circles which are the bases of the cone shaped vortices . this pelvic action drives the femurs in a reciprocating motion reminiscent of the reverse of the action of the steam pistons of an old fashioned locomotive driving its driving wheels , with the additional complexity that the knee ends of the femurs aren &# 39 ; t fixed , as are the ends of steam pistons , but are themselves moving in their own forward rolling circles . the structure we have described supports part of the weight of the rider &# 39 ; s body while it permits the unrestrained natural running action of the pelvis . this three - dimensional articulation is illustrated as deconstructed into three two - dimensional views in fig1 , 19 , and 20 . the double vortex gyration of the structure , in sympathy with the pelvis , when seen in two dimensions from above in plan view in fig1 appears , as shown by double ended arrows , as a reciprocating , ( right side forward , left side aft , then left side forward right side aft ) partial rotation around the center point of the transverse beam , which point corresponds to the pivot point of the pelvis at the base of the spine . the right and left rotational arrows indicate the resulting turning of the pedals . the structure in side elevation view , fig1 , shows a horizontal fore and aft double headed arrow indicating the same reciprocating action as the arrows in fig1 , with the addition of a vertical double headed arrow indicating the simultaneous rocking side to side of the transverse beam , right side higher , left side lower , then left side higher , right side lower . in combination , these motions allow for the forward rolling circular motion common to the human femur sockets of the pelvis and the right and left ends of the transverse beam , as indicated by the rotational arrow . again , the lower rotational arrow indicates the turning of the pedals . the structure in rear elevation view , fig2 , shows vertical double headed arrows indicating the side to side rocking of the transverse beam . in this two - dimensional view the pedals also appear , as indicated by double headed arrows , to be moving in an up and down reciprocating action . however when the information illustrated in all three two - dimensional views is combined , the correct idea of the pedals moving in forward rolling circles 180 degrees out of phase with each other emerges , as does the correct idea of the seat structure &# 39 ; s transverse beam gyrating around a central pivot with its ends moving in forward rolling circles 180 degrees out of phase with each other . in fig2 , 22 , and 23 , three - dimensional information is again deconstructed into three two - dimensional views . each view shows a double headed arrow passing through the base of the spine and the left and right ischeal tubularities and the left and right femur sockets of the pelvic bone . these arrows represent what is called above the horizontal axis of the pelvis . as shown , this axis is parallel to the transverse beam of the seat structure , and maintains this parallel relationship throughout the pedaling cycle . through the pedaling cycle , the lower surface of the buttocks , the skin and muscle covering the rider &# 39 ; s ischeal tubularities , which is the surface bearing the rider &# 39 ; s weight , is continuously changing its tilt from nearly level to a forward cant and back again as the pelvis gyrates . the buttock supporting seat parts of this structure , whose mounts allow them to tilt in any direction and rotate independently from the transverse beam on whose ends they are mounted , maintain constant contact with the lower surfaces of the buttocks and tilt and rotate relative to the transverse beam exactly in sympathy with the buttocks throughout the pedaling cycle , and thus do not rub against them . therefore no friction is created between the rider &# 39 ; s skin and this structure . as illustrated in fig2 , 22 , and 23 , during a pedaling cycle , the structure that we have described permits free motion of the body in an unrestrained way much like the motion of the body during running . during the pedaling cycle , the ischial tubularities of the pelvic bone need to move independently of one another . for example , their vertical positions relative to one another changing continually from the left side of the pelvic bone being higher than the right side , the two sides being at the same elevation , to the right side being higher than the left side , and back through the same elevation , returning to the left side being higher than the right . during the pedaling cycle , there is cyclical fore and aft motion of the two sides of the pelvis . the motion varies from the left side of the pelvis being forward of the right side through the left side and right side being at the same positions fore and aft through the right side being forward of the left side and back through being in the same positions fore and aft and then with the left side forward of the right side again . also , during each pedaling cycle , the canting of each of the femurs , and therefore the skin of the buttocks and the bottoms of the thighs vary cyclically . for each leg , the angle of the femur varies from being approximately horizontal to being canted down in the front relative to the back of the femur and then returning to the approximately horizontal position . these three cyclical motions — the left and right sides of the pelvis moving up and down relative to one another , the left and right sides of the pelvis moving fore and aft relative to one another , and each of the femurs canting up and down itself and in an opposite sense from the canting up and down of the other femur — all occur simultaneously through the pedaling cycle , making for a complex gyrating motion . the mountings of the seat parts on the transverse beam and of the transverse beam on the seat post of the bicycle and the freely permitted motion of them assures that the pelvic and femur cyclical motions are accommodated freely , without resistance , and without friction between the seat parts and the buttocks and thighs . this complex motion is also illustrated in fig2 . when the pedal is at two o &# 39 ; clock ( the first line of cells in fig2 ) the right pelvis ( we sometimes use the word pelvis interchangeably with the word buttocks ; what were referred to as the pelvises are also sometimes referred to as ischial tubularities of the pelvis ; sometimes , when we refer to buttocks , we are also referring to the muscle and skin that covers the ischial tubularities ) is forward of the left pelvis , the right pelvis is higher than the left pelvis , the right femur is approximately horizontal , and the left is canted downward . when the pedal is at five o &# 39 ; clock , the right pelvis is slightly forward of the left pelvis and is slightly lower than the left pelvis , and the right femur is canted down while the left femur is approximately horizontal . when the pedal is at eight o &# 39 ; clock , the left pelvis is forward of and higher than the right pelvis , and the right femur is canted down slightly and the left femur is canted up slightly . when the pedal is at 11 o &# 39 ; clock , the right femur is slightly behind and higher than the left femur , the left femur is canted down , and the right femur is approximately horizontal . one could describe this motion during the pedaling cycle as the left pelvis and the right pelvis following roughly circular gyrating paths around the point at which the center of the transverse beam is mounted on the ball . the two gyrating paths are in a 180 ° phase relationship to one another . the cants of the femurs are also oscillating in opposite phases , up and down . a wide variety of other configurations of the parts in their assembly are also possible alternatively or in combination with the ones described above . in some examples , as shown in fig2 , 26 , and 27 , a cylindrical shaft 110 , seen vertical in front elevation , leans toward the rear of the bicycle to the same degree as the bicycle &# 39 ; s own seat post in side elevation , and has a diameter that fits into the seat post so that its height can be held in proper adjustment by the bicycle &# 39 ; s own seat post clamp . the upper end of the shaft connects to a horizontal beam 112 , which cantilevers toward the rear of the bicycle and extends far enough to position the rider a comfortable distance from the handlebars . the cantilevered beam connects to the upper end of the shaft and cantilevers toward the rear of the bicycle 3 ″ ( q 1 ), for example , from the centerline of the shaft to the center of the opening 115 of the block 114 . the beam may be made of the same material as the shaft and rigid , or it may be made of a material which is stiff enough to adequately support the rider while springy enough to provide a shock absorbing suspension . the rear end of the beam supports and is fastened to a block 114 , as shown in fig2 , 29 , and 30 , which is taller than long and longer than wide , and which is perforated transversely by an opening 115 which is taller than wide and whose edges are rounded in both side elevation and plan view , such that it accommodates a transverse beam that includes two sides 116 and 118 , as shown in fig2 , 26 , and 27 , in a way that allows the beam to gyrate in the opening to a degree which allows the rider all desired mobility , but doesn &# 39 ; t allow the beam to tip toward the front or rear of the bicycle . block 114 measures 2½ ″ high ( m ), 1⅝ ″ long ( n ), and ⅝ ″ wide ( 0 ), and is perforated by opening 115 which measures 1⅞ ″ high ( p ) by ⅝ ″ wide ( q ), for example . the transverse beam 116 and 118 , as shown in fig3 and 35 , is made of two flat pieces which , when bolted together , fit through the hole in the perforated block 114 , with enough clearance to allow the beam to gyrate with slightly more than the maximum gyration required by the rider &# 39 ; s pelvis in pedaling . the two identical flat transverse beam parts 116 and 118 measure ¼ ″ thick ( r ) by 5½ ″ long ( s ), for example . at the ends which are attached to end post and ball elements 120 and 122 , parts 116 and 118 measure 1 ″ high ( t ), which increases to 1½ ″ high ( h ) at a point ½ ″ from the end . this height measurement extends 3¼ ″ toward the far end , at which point it again decreases to 1 ″ height for the rest of its length , for example . the beam is held from sliding through the hole by cheek pieces 124 , 126 , 128 , and 130 , as shown in fig3 , 32 , and 33 , bolted to both sides by the same bolts which hold the beam elements together . the cheek pieces are rounded at their ends 125 , 127 , 129 , 131 closest to the opening in both front and rear elevation views so that they don &# 39 ; t interfere with the gyration action of the beam . parts 124 , 126 , 128 , 130 measure ¼ ″ thick ( y 1 ), 1¼ ″ high ( y 2 ), and 1½ ″ long ( y 3 ). their ends , 125 , 127 , 129 , 131 , are shaped in elevation as ¾ ″ radius half circles ( z 1 ) and in plan as ¼ ″ radius ( z 2 ) quarter circles . the beam elements terminate at their outside ends in posts 120 and 122 , similar to those described in the early are examples , but which require less offset to align them from end to end . the transverse beam sides 116 and 118 , are perforated with respective lines of holes , similar to those described earlier , which are used in the same way to adjust the length of the beam . in some implementations , the rear end of the cantilevered beam supports and is fastened to a short cylinder 216 , which measures 1½ ″ diameter ( w 1 ) and ½ ″ high ( w 2 ), for example , as shown in fig3 and 38 , perforated by a hole 217 at its center and by a circle of shallow holes 219 around its circumference in which flexible solid rubber cylinders 218 , are inserted , and whose upper ends are fitted in matching shallow holes 219 in a matching short cylinder 220 , with a similar central perforation 221 , placed on them upside down . the upper short cylinder supports and is fastened to a block 224 , which is wider side to side than tall and taller than it is thick from front to back . block 224 measures 2½ ″ long ( x 1 ), ½ ″ thick ( x 2 ), and 1½ ″ high ( x 3 ), for example . the block is perforated by a ¼ ″ diameter hole 225 which aligns with the central holes 223 in the two matching short cylinders 216 and 220 . the same hole continues in line through to the bottom of the cantilevered beam or spring . a dacron cord 222 , or other flexible line of a non - stretching material passes through all of these aligned holes and is pulled tight and held tight by knots 227 or other line stopping devices at its ends , so that the rubber cylinders are held in compression . the rubber cylinders are of a length to allow clearance between the short cylinders so that the block at the top can gyrate relative to the cantilevered beam . flat transverse beam elements 228 and 230 , are bolted to the top block in a way similar to those described earlier . in some examples , the short cylinders of the third embodiment contain between them a coiled spring 310 , as shown in fig3 , which is attached to each of them , similarly allowing the attached upper block to gyrate relative to the cantilevered beam , but obviating the need for a central tension cord . the ends of the transverse beams in various implementations may have ball and socket joints to connect them to the seat sections , as in the first examples that we described , or they may be attached to the seat sections with devices similar to the central transverse beam to cantilevered beam joining devices of the later examples , allowing the seat sections to gyrate relative to the ends of the transverse beams . although the examples discussed above are of seats for bicycles , similar seats can be mounted in similar ways on any of a wide variety of other devices on which people sit . such devices can include cycling devices in which the buttocks and legs move cyclically in a motion that is similar to or akin to the motion that occurs during running . such cycling devices can include bicycles , unicycles , tricycles , and human powered aircraft , to name a few . the cycling devices can include devices designed to move the entire user from one place to another , and devices in which the user remains in the same place while the cyclical motion is occurring , such as a wide variety of exercise devices . furthermore , devices that have seats and in which the user &# 39 ; s buttocks and legs are moving continually or only from time to time and are not necessarily moving cyclically can benefit from the concepts that we have discussed , for example , seats in trucks or boats or other vehicles , office and work chairs , and other kinds of chairs . other implementations are also within the scope of the following claims .