Abstract: The present invention includes a tubular body member with a central bore which has two spiralling or threaded interior surfaces, each interior surface having a leading edge at nearly right angles to the longitudinal axis of the body and a sloped or tapered trailing edge along the bore from an end portion toward the central portion of the bore. The upper portion of the body has a left-hand spiralling or threaded surface. The lower portion of the body has a right-hand spiralling or threaded surface. Inserted into the central portion of the body member from each end is a slip segment or member. The outer surface of the upper slip segment has a left-hand spiralling or threaded surface, whereas the outer surface of the lower slip segment has a right-hand spiralling or threaded surface. Each such spiralling or threaded surface conforms to the spiralling or threaded surface of the corresponding interior surface of the stabilizer body.

Abstract: A single tapered bushing system for receiving and mounting a shaft within a bearing assembly is disclosed. A rotatable quill member having a hollow hub is received by the bearings. The hub has a tapered inner bore. A single sleeve having a flange at one end thereof, a tapered outer surface, and a cylindrical inner bore is received within the hub bore, with the outer tapered surface of the sleeve contacting the tapered hub bore substantially along the full length of the sleeve. A longitudinal slot in the sleeve permits circumferential contraction or expansion of the sleeve within the tapered hub bore. The inner sleeve bore receives a shaft in such manner as to accommodate variations in alignment, concentricity, and parallelism, within a limited range, between the axis of the shaft and the axis of the hub. A key and slot arrangement is provided for rotatably coupling the shaft and the hub.

Abstract: A flanged bushing mounting adaptor for use in mounting a flanged bushing in the hub of a shaft-mountable structure, the hub having a tapered bore with recesses formed therein, and the bushing having a tapered barrel and a flange with threaded and unthreaded holes therein. The adaptor has a tapered outer circumferential surface for wedging engagement with the oppositely tapered hub, and a tapered bore for wedging engagement with the oppositely tapered barrel of the bushing. The adaptor also includes a plurality of threaded bores corresponding to the unthreaded holes in the flange, for receiving screws or bolts to secure the bushing to the adaptor and to draw the assembly into the hub. Bosses, or recesses with set screws, corresponding to the recesses in the hub, may be included on or in the outer surface of the adaptor to prevent relative rotation between the adaptor and the hub.

Abstract: A self-tightening shaft coupler includes a rigid, elongate coupling sleeve having an externally compressible collet threaded into each end. The collets engage the ends of the shafts which are to be joined such that the shafts are coupled to one another through the coupling sleeve. The threading of the collets and the coupling sleeve is such that rotation of the shafts in a predetermined direction tends to tighten the collets onto the shafts whereby self-tightening action is achieved.

Abstract: A body portion of a device has an opening for receiving an engaging member and a portion of the body portion defining the opening is distortable into the opening. A wedge is provided in a tapered bore in the body portion adjacent the distortable defining portion and is arranged to distort the latter into engagement against an engaging member. The distortable portion comprises a tab formed by areas of removed material provided between the opening and the tapered bore.

Abstract: A ball stop is locked to a cable by inserting the cable through an opening in the ball. The ball is then rigidly clamped in place by a wedge which is inserted into the aperture surrounding the cable and threads in the aperture and on the external part of the wedge mate and are screwed together to cam the wedge into frictional engagement with the cable.

Abstract: A device for connecting a wheel or wheel-like body to a shaft has tapered inner and outer wedge rings that can be formed over one another using a captive nut. An expanded inner ring has axial slits and fits over the shaft. The inner ring has a tapered outer peripheral surface portion and a threaded cylindrical portion extending along the shaft. An expandable outer ring has a plurality of part-cylindrical segments and can be inserted between the inner ring and the wall of an axial bore in the wheel or wheel-like body. The outer ring has a tapered inner surface which is complementary to the tapered outer surface of the inner ring. The outer ring has a first annular groove formed in its inner peripheral surface adjacent to its minimum inside diameter end and a second annular groove formed in its outer peripheral surface. The segments are held together by a retaining ring fitted in the second annular groove of the outer ring.

Abstract: A device for providing a clamping joint comprises two elements (1,2) with complementary threads, each having a flange constituting a clamping surface. Clamping takes place upon relative axial displacement of the elements (1,2) which can be brought about by screws (4) arranged axially in bores in a flange (5) on one element. In order to prevent accidental disengagement of the elements, at least one of the threads adjoins at one end to a part (6) which is wedged against an opposing thread flank when the elements (1,2) are rotated in relation to each other over a predetermined end position.

Abstract: An extractor for an increment borer (1), which increment borer (1) consists of a tubular body having internally a cylindric portion, which transforms to a conic portion (6), and which on the outside is provided with bore threads (4). According to the invention, an end piece (10) is provided for being attached to and detached from the rearward end of the blade (9). The end piece comprises a sleeve (12) and a domed nut (14), each of which are provided with threads (13,15) arranged so, that the sleeve (12) and domed nut (14) are axially movable relative to another. The end piece (10) further comprises an oblong conic locking pin (16) intended to be inserted together with the rearward end of the blade (9) into an axial through hole in the sleeve (12). The domed nut (14) is intended at its threading on the sleeve (12) to axially move the locking pin (16), which thereby is pressed against the blade (9) located between the locking pin (16) and the wall of said hole of the sleeve (12).

Abstract: In a torque transmitting assembly including a driven member and a driving member, one having teeth thereon extending parallel to the rotational axis and the other having teeth thereon extending obliquely to the rotational axis, an annular member is interposed which also has teeth which are parallel to the rotational axis and oblique to the rotational axis for engaging with the corresponding teeth of the driving and driven members in order to place them in torque transmitting engagement with each other. The annular member is formed from a deformable metallic material and the obliquely extending teeth extend relative to the parallel teeth at an angle of between 15.degree. and 45.degree..

Abstract: The apparatus comprises a first conical ring which acts from the inside against a radially thin walled portion in the center opening of the disk and a second conical ring which acts against a radially thick walled partial area located adjacent the disk. The thin and thick walled portions are part of a flanged hub ring which is connected with the disk by bolts.

Abstract: A telescoping steering shaft includes a first shaft (16) having a polygonal-shaped bore (18) receiving for reciprocation therein a polygonal-shaped second shaft (12) having a tapered end (13). The polygonal-shaped second shaft (12) has a through axial opening (14) receiving a connecting rod (20) therein, the rod having a nut-shaped end (26) located adjacent the tapered end (13) of the second shaft (12) and the other end (15) being threaded to receive a lever (24) thereon. A collet nut (31) is mounted on the rod (20) adjacent the nut-shaped end (26) and has a plurality of axially extending projections (36) each including at least one surface (37 or 38) disposed parallel to an adjacent surface of the polygonal bore (18) and an interior axially inclined surface (35) disposed adjacent the tapered end (13).

Abstract: The caliper (52), in the form of a closed frame surrounding the fixed support (50), incorporates at least one axial reinforcing member (3) joining two axially separated zones (1, 2) of the caliper by passing through them and extending radially beyond the periphery of the disc (53). The reinforcing member incorporates a head (4), which is received within a complementary recess in the first zone of the caliper (1), and a threaded end cooperating with first and second locking and tightening elements, cooperating with each other (for example a locking nut 5 and a removable washer 10) of which the first elements is lockable on the threaded end so as to give, together with the second element, a predetermined tension to the reinforcing member, the second element being capable of being selectively disengaged to allow the reinforcing member to be separated (by tilting or longitudinal displacement) from the second zone (2) of the caliper.

Abstract: A friction-transmitting shaft/flange connection has a pressure ring arranged to be seated on a shaft and having a conical ascending surface, and a clamping ring having a pressing surface with which it is clamped on the ascending surface of the pressure ring and an end surface which is simultaneously connected with the flange in a friction transmitting manner.

Abstract: The pan head consists of a single tube for supporting the tilt arm and the table in mutual rotatable relationship. A knob is attached to the rod for retaining the table and tilt arm against separation by withdrawal of the axis tube from its bore and also for urging the tapered pieces into the open end of the tube for interlocking the table and tilt arm.

Abstract: A clamping device for the fastening of a hub on a shaft, with a tapered flange ring having a cylindrical circumferential surface, with a conical circumferential surface radially opposing the surface and with a radial flange and with two taper parts capable of being tightened by means of axial clamping screws, with conical surfaces intended for cooperation with the tapered surface of the tapered flange ring. Control of the stress distribution along the shaft and security against overloads without slipping on the shaft are also obtained.

Abstract: A support for endless grinding sleeves for grinding workpieces has a casing which axially running slots or grooves and the support has a round outline in cross section. An axial hole through the support becomes narrower along its length and is designed to receive a wedging cone that is to be drivingly joined with a shaft. The outer surface of the support is made somewhat smaller in size than the inner circumference of the endless grinding sleeve that is to be placed on the support and the cone is driven into the support to radially expand it into engagement with the sleeve.

Abstract: An improved upper member for the two-part ball race of a bicycle headset is provided which is light in weight and has a ball engaging surface which follows closely the contours of the balls.

Abstract: A bearing assembly and method of installing such within an enclosing open walled chamber wherein the bearing assembly utilizes first and second spaced apart bearing units. The bearing units low frictionally rotationally support a crank. The inner races of the spaced apart bearing units are connected together through a sleeve which is located about the crank. Mounted on the outer race of each bearing assembly is an expanding ring assembly. Each expanding ring assembly can be moved into tight engagement with the wall of the chamber.

Abstract: A device for coupling a shaft and the hub of a machine element such as a pulley or gear for joint rotation, includes annular outer and inner wedges each of which has angularly spaced longitudinal slots, and ribs aligned with the slots. The wedges telescope so that the ribs of one wedge extend into the slots of the other, aligning longitudinal bores of the ribs to receive fastening elements such as screws. The fastening elements thus impart relative axial movement to the wedges to expand the same radially into gripping engagement with the shaft and hub.

Abstract: A split, circular flanged bushing for securing driving or driven elements such as sheaves, pulleys, and the like to a rotatable shaft, having an integrally formed key in the center opening of the bushing for insertion in a corresponding keyway in the shaft. The bushing is formed in a sintering operation and increased density is imparted to fillets or junctions between the flange and the outer wall of the body, thereby providing increased resistance to stress fatigue in these critical areas. Fillets between the key and the inner wall of the body are provided to distribute the stress concentration inherent in these areas.

Abstract: A novel device for clamping together a sandwich-type gel slab plate assembly includes an elongate housing having a recess on one side and two movable bars placed parallel to each other inside the recess. Due to a series of angled parallel surface segments on the lateral edges of the bars and one side wall of the recess, a vertical force against one bar translates into a lateral force against the other, urging the latter toward the other side wall of the recess, clamping the plates in between with even force along the entire length.

Abstract: A locking mechanism for a telescopic steering wheel which includes a housing, an outer cylinder rotatably supported within the housing, a locking member slidably mounted within the outer cylinder, a steering shaft movably mounted within the outer cylinder, engaged with the locking member and operatively connected to the steering wheel, a locking rod rotatably mounted in the steering shaft and engaged with the locking member for attaining a locked or unlocked position of the locking member, a telescopic lever connected to the locking rod and movable between the locked and unlocked position and a mechanism for continuously urging the telescopic lever into the locked position.

Abstract: A circular coupling for interconnecting a shaft to a bearing is disclosed. The coupling comprises a coil having a plurality of turns adapted to surround the shaft, as positioned within the inner race of the bearing. The coil is axially compressed for displacing coil turns relative to one another to frictionally bind the shaft to the bearing inner race. Upon releasing the compression on the coil, the bearing shaft may be removed from the shaft.

Abstract: There is described a vibrating railroad ballast tamping tool head which provides ease of replacement of tamping tools, in the field. The head according to a preferred embodiment has a tamping tool holder mounted centrally on the end of a tool drive shaft, a pair of spaced tamping tool-shank receiving sockets being provided in the holder one on either side of the drive shaft and open to the underside of the holder. A pair of tamping tools each having a lower ballast engaging working face and an upper shank are located by means of tapered bores and key ways within each of the sockets and a tamping tool retaining yoke engages the shanks of both tamping tools underneath the tool holder and locks the tools to the holder by means of a centrally disposed bolt which is received in a blind bolt hole in the holder and draws up to force the tools into the sockets and to lock them therein.

Abstract: A device for mounting an aircraft engine and a propeller on a longitudinal member or fuselage of a lightweight aircraft. A sleeve is disposed about the longitudinal member and securing devices which prevent longitudinal movement of the sleeve relative to the longitudinal member are positioned at either end of the sleeve. Vibration dampening rings are disposed between the securing devices and cups which can be threaded along the sleeve placing the rings in the desired compression. The engine and the propeller are mounted on the sleeve. A driving sleeve is rotatably mounted on the sleeve and is drivingly attached at one end to the output of the engine and is mounted at the other end to the propeller. The propeller is rotatable about the longitudinal axis of the longitudinal member and the wing structure and tail structure can be mounted on the longitudinal member as well with the propeller positioned between them. The mounting device can also be used for biplanes.

Abstract: A bushing and hub assembly for mounting sheaves, sprockets, gears, couplings and similar machine elements on a shaft, wherein two types of tapered bushings are used, the bushings having bodies of the same taper used with a single hub which is compatible with both bushings. One of the bushings has a radially extending annular flange at the large end of the tapered body and the other bushing is flangeless. The screw holes and plain holes are provided in the flange and at the interface of the bushing and hub for securing the selected bushing in place in the hub for mounting the machine element on the shaft with screws for tightening the bushings securely in place on the shaft and in the hub bore. The two bushings and the sidewalls of the hub all have the same taper and are interchangeable with one another, to provide optimum performance and convenience of installation.

Abstract: A connection unit, which may be undone, for rope ends and more particularly ropes in the form of belts for driving systems, rope conveyors or ropes for lifting loads has, as part of a preferred example, a plate with two rope keepers supported on pins and which keep the rope ends in position thereon by way of stops. These rope end keepers or takeup parts are designed so that they may be turned and locked in position so that, dependent on the direction of turning, the rope may be taken up and made shorter or let off and made longer. The plate, as part of a further example of the invention, has guide parts for positively guiding the rope end and furthermore there is a guiding structure, designed to match the form of a driving sheave so that it may be run thereover.

Abstract: A corrosion resistant shaft and boss clamping device comprises an inner race to be fit over the shaft, an outer race to be fit inside the boss enclosing the shaft and the inner race, the races having wedge-shaped surfaces facing one another, a pair of taper rings having a complementary wedge shape disposable between races, and, bolts adapted to urge the taper rings toward one another, thereby clamping the shaft to the boss. The inner and outer races are expansible and contractable, being made of split rings of austenitic stainless steel. The clamping bolts are made of precipitation hardened stainless steel, and one of the taper rings is provided with a hardened nitrided layer on the surface thereof to be contacted by the clamping surfaces of the clamping bolts.

Abstract: The invention refers to a device for torque transmitting interconnection of two shafts (1, 2) or the like. The shafts are at their opposite ends provided with flanges formed as clamping sleeves incorporating inner and outer sleeves (7 and 6 respectively), the inner sleeve of which is clamped against the shaft at a relative axial displacement of the sleeves. Power transmission takes place via a number of axial pegs (5) which extend between recesses in each flange. A part of each recess is situated in each of the inner and outer sleeves whereby a relative rotation of the sleeves is prevented by the pegs, and the resistance of the inner sleeve against clamping is reduced.

Abstract: An expansion dowel assembly is formed of an axially extending dowel body and an expansion member. The dowel body has a support surface inclined relative to the axis of the dowel body along which the expansion member can be displaced for anchoring the dowel assembly in an opening such as a borehole. At least a portion of the support surface is in the form of a groove extending in the axial direction of the dowel body and the bottom of the groove is inclined so that the expansion member is forced radially outwardly away from the axis of the dowel body as it is displaced through the groove.

Abstract: A pivot pin assembly according to the teachings of the present invention is shown in use in a mobile tree felling and handling device. A pivot pin is held between first and second support members. In the preferred embodiment, the pivot pin assembly includes first and second bushings having an outside male tapered surface and having an internal bore for slidable receipt on the pivot pin. The bushing in its most preferred form includes a cut which extends through the outside male tapered surface and terminates in the internal bore to split the bushing along a radius to form a caliper-like member having first and second legs with their free ends in a spaced relation. The support members include a female tapered opening having a size and shape complementary to and for receipt of the outside male tapered surface of the bushing.

Abstract: A speed reducer having a power takeoff sleeve loosely receives therein a shaft to be driven. Concentricity and a driving connection of the shaft and sleeve is effected by a pair of telescoping bushings having tapered interfitting surfaces in each end of the sleeve. The inner bushing of each pair is split and grips the shaft when drawn into the outer bushing by screw threaded means. The outer bushings are concentric with and rotatable in the sleeve ends and keyed therein to preclude axial movement. In a first modification the inner split bushings are keyed to both shaft and sleeve and in a second modification the shaft is keyed directly to the sleeve.

Abstract: A system and method of mounting a lamp holder on a support in such manner that the fasteners or other securement means are hidden from view. Specifically, the system includes a pair of wedge-locking mounting brackets, one of which is secured on place on the support (e.g., on a vertical lamp post or on the outer end of a horizontal support arm) and the other of which is secured on a lamp holder (e.g., either on a horizontal lamp support arm which is to be secured to the post or on a lamp which is to be secured to the horizontal support arm) so that upon bringing the lamp holder into abutting relation with the support and upon effecting relative vertical movement between the lamp holder and the support, the former is wedgingly drawn into secure abutting relation with the latter and so that the mounting bracket is hidden from view. A method of mounting a lamp holder is also disclosed.

Abstract: An anchor pin assembly (100) for a drum brake (10) is provided. The anchor pin assembly is mountable to a drum brake spider (14) provided with an anchor pin receiving bore (34). The assembly includes two anchor pin pieces (102 and 104) having inclined ramps (116 and 118) formed on the inner ends thereof, an expansion member (120) having mating ramps (122 and 124) formed thereon and a bolt (132) and nut (138) for applying an axially inward compressive force to the pieces to cause radially outward expansion of the expansion member.

Abstract: A locking device for securing a straddle-type adapter to the lip of an excavator wherein the C-clamp and wedge have cooperating arcuate surfaces and are bolted together whereby tightening the bolt moves the wedge on the arcuate surface of the C-clamp to tighten the fit of the adapter on the lip.

Abstract: An improved device is disclosed for connecting a plunger to a connecting rod of the type having a crosshead connected to the connecting rod, the crosshead having a coupling element with a flange and a coupling nut mounted to the flange. The coupling element is provided with a centering bore and a thrust plate is mounted to the coupling element. The thrust plate has a first side with a centering stud extended into the centering bore and an annular shoulder surrounding the centering stud seated against the flange. The thrust plate has a recess on a second side opposite the first side for receivingly centering an end of the plunger. A clamping assembly for clamping the coupling element includes a collar threadably engaged to the coupling nut.

Abstract: A structure for securing a cylinder drive gear to a cylinder shaft in a printing machine comprises a cylinder having an end shaft, a cylinder drive gear inserted and fixed by bolts onto said end shaft, a pair of taper rings with their taper faces being in contact with each other, one of said taper rings being mounted on said end shaft such that the movement in the axial direction is limited by said cylinder drive gear, another taper ring being mounted slideably on said end shaft, and a device for tightening said another taper ring toward said cylinder drive gear so that both taper rings expand in the radial direction.

Abstract: The invention concerns a device for providing a friction joint. It comprises an inner (1,11) and an outer (2,9) element, the inner element having a tapered outer surface co-operating with a complementary tapered inner surface in a bore in the outer element. Means (6,7,8,12) are provided for displacing the elements axially parallel to the taper axes. One element preferably consists of a slitted clamping sleeve, and for diminishing the friction in the tapered contact and simplifying manufacturing of the parts of the device, one of the tapered surfaces is provided with a friction reducing material and one of the tapered surfaces has a groove (3,4,5,13,14,15,16) extending around the circumference.

Abstract: The invention refers to a device for producing a friction joint incorporating two members (1,2) having concentric opposite and mainly tapering surfaces, which are squeezed against each other at a relative axial displacement in one direction. The joint preferably incorporates a sleeve, on which one of said surfaces is arranged and for obtaining a minimum radial extension are the joint surfaces in longitudinal section provided with a saw tooth contour, which can be formed by a number of taper portions arranged in a row or by a helical ramp (6), which forms an angle to the center axes of the members.

Abstract: The invention relates to a clamping arrangement to connect a hub with an inner structural part, in particular a shaft, including at least one outer taper ring having an inner conical surface tapered at a self-returning angle. The tapered ring cooperating with a tapered outer circumferential surface of a tub. Axially acting lock bolts, tension the tapered ring against the hub locking the assembly to the shaft. Wedge segments, distributed circumferentially and arranged axially between the taper ring and a counter-support on the hub, are provided. The wedges are displaced radially by means of radial release bolts and pressure the tapered ring axially off the conical surface of one hub releasing the same from the shaft.

Abstract: A friction connection is formed between an annular member such as a wheel, pulley or the like and a shaft by at least one annular wedge which clamps the annular member to the shaft by translating axial pressure from wedge-tightening screws into radial clamping forces. According to the invention, the annular member is provided with a groove centered on the axis of rotation and receiving an open measuring ring at least partly slidable in the groove, the relative spacing of the ends of which serves to indicate the radial clamping force.

Abstract: An electromagnetic single-surface clutch/brake combination, especially for textile machinery, in which a rotor assembly is locked to the shaft end encloses the magnetic body carrying the coils so that the latter can be secured to the housing flange when the unit, as delivered, is mounted on the shaft. The rotor assembly and the magnetic body are bridged by a bearing.

Abstract: A power transmission device for internal combustion engine including a timing belt pulley for a timing belt which drives cam shaft and so forth, and a pulley for V belt for driving auxiliary machineries such as cooling fan, the timing belt pulley and the pulley for V belt being attached to an end portion of the engine crank shaft. One of these pulleys is fixed directly to the engine crank shaft, while the other is fixed to the first-mentioned pulley which is fixed to the crank shaft.

Abstract: Cone-coupling for interconnecting a hub (4) and a shaft (5) and comprising an outer cone sleeve (1) and an inner cone sleeve (2) designed for being clamped together by means of screws (3), whereby at least one of the cone sleeves is brought to move in the radial direction for interconnecting the hub (4) and the shaft (5). The radially moving cone sleeve or cone sleeves (1, 2) are formed with several axial slots (16, 17) extending through the material of the sleeves, and the said sleeve or sleeves (1, 2) are formed with a weakened deformation portion (18, 19) located axially outside the hub (4) to be connected to the shaft (5) and allowing a radial parallel displacement of the slotted sleeve portions (14, 15).

Abstract: To permit acceptance of diametrically directed clamping forces of a double-acting hub-to-shaft clamping connection in which an inner ring is formed with outer conical surfaces, an outer ring formed with inner conical surfaces, and clamping or compression rings with matching conical surfaces are positioned between the conical surfaces of the inner and outer ring, a circumferentially continuous cylindrical metal ring is provided formed with a circumferential groove fitted either over (FIG. 2) the outer ring, or within (FIG. 3) the inner ring to permit application of the structure over a stub hub, or within a hollow blind recess or bore (FIG. 3) of the shaft (5).

Abstract: The invention refers to a fastening sleeve for fastening machine members such as bearings or gear wheels to a shaft. The fastening sleeve is characterized by a body of pressed sheet metal, which is embedded or encapsulated in a housing made of plastic material. One surface of the fastening sleeve is tapering and one axial end of the body is free from moulding compound projecting outwardly beyond one axial end of the plastic housing.

Abstract: The disclosure is of a device for connecting the handlebars to the steering fork of a bicycle.

Abstract: A tapered bushing and hub assembly for mounting on shafts sheaves, gears, sprockets, couplings and similar machine elements, in which a tapered, split bushing is inserted in a tapered bore in the machine element and a plurality of lugs secured by screws onto the hub force the bushing inwardly into the tapered bore, seating the bushing into face-to-face contact with the tapered surface of the hub and contracting the bushing firmly onto the shaft. Holes for the screws are provided in the hub and are arranged parallel with the axis of the bore, and preferably extend through the hub. Each lug bears against the side of the hub and the large end of the bushing as the screws are tightened into their respective holes. When the machine element is to be removed from the shaft, a lug may be secured by the screws on the opposite side of the hub to force the bushing outwardly from the tapered bore.

Abstract: A roll device includes a roll shaft and at least one roll ring mounted on the roll shaft. A lock means is securable to the roll shaft. A centering element is disposed between the roll ring and the roll shaft to center the roll ring. A first resilient element is axially interposed between the lock means and the centering element. A second resilient element is axially interposed between the lock means and the roll ring. The lock means applies axial force to the first and second resilient elements to position the centering element relative to the roll ring and roll shaft, and clamp the roll ring to the roll shaft for common rotation therewith. The spring rates of the first resilient element can be made less than that of the second resilient element to regulate the relative amount of axial forces applied to these elements.