Abstract: The present disclosure relates to adapter assemblies for use with and to electrically and mechanically interconnect electromechanical surgical devices and surgical loading units, and to surgical systems including hand held electromechanical surgical devices and adapter assemblies for connecting surgical loading units to the hand held electromechanical surgical devices.

Abstract: The present disclosure relates to adapter assemblies for use with and to electrically and mechanically interconnect electromechanical surgical devices and surgical loading units, and to surgical systems including handheld electromechanical surgical devices and adapter assemblies for connecting surgical loading units to the handheld electromechanical surgical devices.

Abstract: A ball-CV style transmission suitable for use in a Positive Displacement Motor (PDM). A shaft provides shaft wings received into housing receptacles on a housing. A ball and a Torque Transfer Element (TTE) is interposed between each shaft wing and housing within each housing receptacle, with the ball received into opposing recesses preferably on the shaft wing and the TTE. The TTEs float within their corresponding housing receptacles so as to maintain torque transfer contact between all thrust surfaces during articulated rotation of the shaft with respect to the housing. The TTEs preferably float generally radially towards the shaft centerline as angular deflection increases during articulated rotation.

Abstract: The present disclosure relates to adapter assemblies for use with and to electrically and mechanically interconnect electromechanical surgical devices and surgical loading units, and to surgical systems including handheld electromechanical surgical devices and adapter assemblies for connecting surgical loading units to the handheld electromechanical surgical devices.

Abstract: A transmission for a lawn mower, for transmitting an output of a drive source to a driving wheel, the transmission including a speed-change transmission device and a power transmission device movably coupled to the speed-change transmission device. The power transmission device includes a first power transmission device coupled to the speed-change transmission device and a second power transmission device to which the driving wheel is coupled, and the first power transmission device and the second power transmission device are movably coupled to each other.

Abstract: A rod cluster control assembly having a control rod upper end plug formed in two parts and connected together with a flexible joint coupling located at or below a connecting finger on a spider vane. The upper portion of the upper control rod end plug is screwed into the connecting finger on the spider vane and lock welded between a lower portion of the finger and a shoulder on an abutting ledge of the upper portion of the end plug.

Abstract: An arrangement transmits a torque between a shaft and a hub. The hub has at least approximately the interior geometry of an equilateral n-sided polygon, the side surfaces of which at least approximately bear against a clutch portion, which is of circular overall cross section, of the shaft, and wherein the shaft has at least one driver portion which is rotationally conjoint with respect to the clutch portion and which extends in the direction of a corner of the n-sided polygon.

Abstract: A universal coupling is provided that aims to achieve constant velocity between the input and output shafts. The universal coupling also aims to increase the angle between input and output shafts over conventional double Cardan joints while maintaining constant velocity or near constant velocity therebetween. The universal coupling can employ a Sarrus type linkage in-between two universal joints of the Cardan type in a configuration that aims to achieve joint angles up to and including 90 degrees in the Y-Z plane, while maintaining constant velocity or near constant velocity therebetween.

Abstract: A constant velocity joint includes an outer housing and an inner race disposed inside the outer housing and spaced therefrom. The outer housing and inner race are respectively rotatable about a first and second rotation axes, and moveable relative to one another to change an angle between the rotation axes. A cage, disposed between the outer housing and the inner race, has cage windows defined therethrough. A plurality of balls, each retained in a corresponding cage window roll along corresponding outer housing grooves and inner race grooves, respectively defined on an inner surface of the outer housing and an outer surface of the inner race. Rotation of one of the outer housing and the inner race about their respective rotation axis, causes rotation of the other. A cooling member disposed on the outer housing contacts at least a portion of its outer surface. Powertrains and vehicles are also disclosed.

Abstract: An arrangement transmits a torque between a shaft and a hub. The hub has at least approximately the interior geometry of an equilateral n-sided polygon, the side surfaces of which at least approximately bear against a clutch portion, which is of circular overall cross section, of the shaft, and wherein the shaft has at least one driver portion which is rotationally conjoint with respect to the clutch portion and which extends in the direction of a corner of the n-sided polygon.

Abstract: A protective screen mounted on an outer cylindrical surface of a constant-velocity joint and facing towards a sealing device of a rolling-contact bearing which is angularly coupled to the constant-velocity joint for protecting the sealing device and the rolling-contact bearing from the action of external agents; the screen being provided with: an annular wall, which is transverse to an axis (A) of rotation of the constant-velocity joint and is arranged in axial abutment against a side wall of said constant-velocity joint, a central hole, which is made through the annular wall and through which a shaft of the constant-velocity joint passes with play, and a plurality of elastic mounting and centering fins, which are distributed uniformly about the central hole and extend unsupported from the annular wall such that they are coupled to the outer cylindrical surface of the constant-velocity joint.

Abstract: An object of the present invention is to enhance assemblability of a wheel bearing device, and stably maintain predetermined torque transmissibility over a long period of time. A shaft portion (12) of a joint outer ring (5) where projections (35) extending in an axial direction are provided is press-fitted into a hole portion (22) of a hub wheel (1) to thereby form recesses (36) by the projections 35 in an inner diameter surface (37) of a shaft fitting hole 22a of the hub wheel (1), by which a recess-projection fitting structure M is constructed, where an entire area of fitting sites of the projections (35) and the recesses (36) are brought into close contact. Moreover, a bolt member (50) is fastened in a bolt hole (13) provided in the shaft portion (12) of the joint outer ring (5) after the construction of the recess-projection fitting structure (M), which restricts separation between the hub wheel (1) and the joint outer ring (5).

Abstract: An input shaft to output shaft coupling including an input shaft having a first wave surface thereupon, wherein the first wave surface comprises mounds and valleys. The coupling additionally comprises an output shaft having a second wave surface thereupon, wherein the second wave surface comprises mounds and valleys. The coupling in one form additionally comprises a housing substantially enclosing the first wave surface and second wave surface, wherein rotational force exerted upon the input shaft is translated through the lobes of the first wave surface to the lobes of the second wave surface and to the output shaft in turn, and wherein the first wave surface and second wave surface transmit rotational force therebetween through any range of angles to a maximum output angle between a rotational axis of the input shaft relative to a rotational axis of the output shaft.

Abstract: A constant velocity joint includes a first rotation body and a second rotation body. The first rotation body includes a cup unit, a shaft, and ribs that project from the cup unit and connect the cup unit to the shaft. One of the first rotation body and the second rotation body transmits a rotational driving force to other one of the first rotation body and the second rotation body through balls. The first rotation body is so formed that the cup unit and the shaft are formed into one piece using resin material. Moreover, the rib is so formed into one piece with the cup unit and the shaft using resin material.

Abstract: A low-end adjusting mechanism for vehicle suspensions useful for compensating rolling and pitching motions and for leveling purposes, in which a vehicle spring (1) having a longitudinal axis is mounted between two spring seats or receptacles (2, 3), and at least one spring seat can be adjusted in the direction of the longitudinal axis of the spring by rod shaped coupling elements which are mounted at both ends in an articulated or pivotable manner.

Abstract: A driving wheel bearing apparatus has an inner ring 5 secured to a wheel hub 1 by a caulked portion 13. An outer joint member 14 of a constant velocity universal joint 3 has a shoulder portion 19 and a cylindrical shaft portion. Face splines 19a and 13a are formed at the end faces of the shoulder portion 19 and the caulked portion 13. Face splines 19a and 13a are supported with pressure by a fastening bolt 21 that abuts the outer side end face of the wheel hub 1 and is threadedly connected to an internal thread 20a of the shaft portion 20. Compressive remaining stress is placed on the surfaces of the face splines 19a and 13a as a result of surface modification, by shot peening. The surface hardness is set at 300 Hv or more.

Abstract: A constant velocity joint assembly and a method of securing a shaft to the assembly are described. The assembly may have an outer race with a first portion having a plurality of grooves and a second portion that extends from the first portion and is substantially parallel to the shaft. The method of securing the shaft to the assembly includes the step of magnetically pulse welding the shaft to the outer race.

Abstract: An outer ring, an inner ring and a ball that are a rolling contact member formed of sintered ? sialon inexpensive and capable of reliably ensuring sufficient durability, is constituted of a sintered body containing ? sialon as a main component and having a remainder formed of an impurity, and the outer ring, the inner ring and the ball have raceway/rolling contact surfaces, i.e., an outer ring raceway surface, an inner ring raceway surface and a ball rolling contact surface included in a portion having an outer ring high density layer, an inner ring high density layer and a ball high density layer higher in density than an inner portion.

Abstract: The present invention relates to a torque transmitting device (10) for transmitting torques between two shaft sections of a shaft arrangement by way of an articulated arrangement (12), wherein the articulated arrangement (12) is designed to compensate for an angular offset between the two shaft sections.

Abstract: A simple, center-less universal joint of ultra tight tolerance comprising two yokes, each having two facing, distinctly round interface surface areas; both yokes being easily engaged (a self aligning process) and disengaged.

Abstract: A driving wheel bearing apparatus has an inner ring 5 secured to a wheel hub 1 by a caulked portion 13. An outer joint member 14 of a constant velocity universal joint 3 has a shoulder portion 19 and a cylindrical shaft portion. Face splines 19a and 13a are formed at the end faces of the shoulder portion 19 and the caulked portion 13. Face splines 19a and 13a are supported with pressure by a fastening bolt 21 that abuts the outer side end face of the wheel hub 1 and is threadedly connected to an internal thread 20a of the shaft portion 20. Compressive remaining stress is placed on the surfaces of the face splines 19a and 13a as a result of surface modification, by shot peening. The surface hardness is set at 300 Hv or more.

Abstract: Disclosed herein is a constant velocity coupling of a new design and manufacture comprising an input shaft having a first wave surface thereupon, wherein the first wave surface comprises mounds and valleys. The constant velocity coupling additionally comprises an output shaft having a second wave surface thereupon, wherein the second wave surface comprises mounds and valleys. The constant velocity coupling additionally comprises a housing substantially enclosing the first wave surface and second wave surface, wherein rotational force exerted upon the input shaft is translated through the lobes of the first wave surface to the lobes of the second wave surface and to the output shaft in turn, and wherein the first wave surface and second wave surface transmit rotational force therebetween through any range of angles to a maximum output angle between a rotational axis of the input shaft relative to a rotational axis of the output axis.

Abstract: A joint assembly has a pair of constant velocity universal joints and a connecting drive shaft. A cover unit protects the constant velocity universal joints and prevents hanging down of the joints under their own weight. The unit cover is arranged to cover the outer circumferential surfaces of the pair of constant velocity universal joints and boots. The unit cover is formed from elastomer material by injection molding. The cover unit inner circumferential surface has a configuration corresponding to the outline configurations of the pair of constant velocity universal joints and the boots.

Abstract: Provided is a constant velocity universal joint having high strength and capable of suppressing deformation caused by quenching at an opening end portion of a track groove of an outer joint member. In an undercut-free constant velocity universal joint in which a track groove (1d) in a cup portion (1a) of the outer joint member has a hardened layer (8a) formed by induction quenching, an opening end surface (1e) is protruded by a protruding amount t in an axial direction from a groove bottom (c) of the track groove (1d) in a relief surface (1f). The protruding amount t satisfies a relation of t=0.037 d to 0.185 d when a diameter of a torque transmission ball is represented by d. The opening end surface (1e) in a protruded portion (1i) and an outer surface (1j) of the cup portion (1a) continuous to the opening end surface (1e) have an unhardened layer free from hardening by quenching.

Abstract: Provided is a bearing device for a wheel capable of suppressing a backlash in a circumferential direction, excellent in coupling workability of a hub wheel and an outer joint member of a constant velocity universal joint, and excellent in strength owing to stable fitting between the hub wheel and the outer joint member of the constant velocity universal joint. An axle module using such bearing device for a wheel is also provided. Projecting portions extending in an axial direction are provided on one of an outer surface of a shaft section of the outer joint member and an inner surface of a hole portion of the hub wheel. The projecting portions are press-fitted into the other along the axial direction, and recessed portions are formed in the other through press-fitting of the projecting portions.

Abstract: A joint arrangement in the manner of a counter track joint, wherein a cage is provided which is arranged between a joint outer part and joint inner part, which has a cage outer sphere with an outer sphere centre point and a cage inner sphere with an inner sphere center point and which has a plurality of cage windows which each hold at least one ball, wherein at least the outer sphere center point and the inner sphere center point of the cage are arranged offset with respect to the joint center plane.

Abstract: The present invention provides a constant velocity universal joint component and a manufacturing method thereof capable of achieving increased strength without significant procedural changes, and that can contribute to size reduction and weight reduction. In the constant velocity universal joint component of the present invention, a sharp-angled portion 15 is formed by machining after cold plastic working is applied. A carburization process is then performed in which surface carbon concentration of 0.45 mass % to less than 0.60 mass % is obtained. Quenching is then performed. High-frequency induction hardening is subsequently performed.

Abstract: A constant velocity universal joint is disclosed that comprises an outer joint part, an inner joint part, torque transmitting balls, an annular ball cage, and a supporting mechanism. The outer joint part includes circumferentially distributed outer ball tracks. The inner joint part includes circumferentially distributed inner ball tracks. The torque transmitting balls are guided in pairs of tracks, wherein each track includes an outer ball track and an inner ball track. When the joint is in the aligned condition, the pairs of tracks, at least in a central joint plane, widen in coinciding axial directions. The annular ball cage is defined by a cage axis. The cage is positioned between the outer joint part and the inner joint part and comprises circumferentially distributed windows in which the torque transmitting balls are held with a clearance. The ball cage comprises an axial clearance relative to the outer joint part.

Abstract: A homokinetic joint includes an outer hub having outer running tracks, an inner hub having inner running tracks, balls which are guided in pairs consisting of an outer running track and an inner running track and a cage having cage windows, in which the balls are accommodated. The homokinetic joint further includes a sleeve that is firmly connected with the inner hub and disposed coaxial to it and sealing means having an accommodation part that is connected with the outer hub so as to rotate with it. The sealing means have a sealing membrane firmly connected with the outer hub by means of an outer collar, and connected with the sleeve by means of an inner collar, forming a seal, and having a securing ring for fixing the inner collar in place on the sleeve. The sleeve has a circumferential annular groove, into which the sealing membrane engages with an inner annular bead that is formed on.

Abstract: A constant velocity joint includes a first rotation body and a second rotation body. The first rotation body includes a cup unit, a shaft, and ribs that project from the cup unit and connect the cup unit to the shaft. One of the first rotation body and the second rotation body transmits a rotational driving force to other one of the first rotation body and the second rotation body through balls. The first rotation body is so formed that the cup unit and the shaft are formed into one piece using resin material. Moreover, the rib is so formed into one piece with the cup unit and the shaft using resin material.

Abstract: A direct torque flow constant velocity joint connector includes an outer joint part, and inner joint part, a cage and a plurality of balls. The outer joint part includes outer ball tracks. The inner joint part includes inner ball tracks and a rotational axis, wherein the inner joint part has a face spline oriented about the rotational axis. The plurality of balls are provided in the cage and engage the inner and outer ball tracks of the respective inner and outer joint parts, thereby allowing torque transmission by way of the face splines. Also provided is a direct torque flow constant velocity joint connection.

Abstract: A control system for a vehicle having first and second wheels is provided that includes a differential apparatus adapted to distribute torque between the first and second wheels and a traction controller for controlling operation of the differential apparatus from vehicle launch up to a predetermined vehicle speed. The traction controller is configured to engage the differential apparatus in a first operating state according to at least one vehicle operating parameter indicative of a low traction operating condition and to further control engagement of the differential apparatus in a second vehicle operating state during the low traction operating condition according to a difference between an actual vehicle yaw rate and a predetermined target vehicle yaw rate. The control system also includes a stability controller for controlling engagement of the differential apparatus at or above the predetermined vehicle speed.

Abstract: An exemplary constant velocity ball joint in the nature of a counter track joint, includes first and second track pairs that form an opposite opening angle (W1, W2), wherein the first track pairs are provided with a track inflection point (P1) and the second track pairs each form a second track centerline (L2) that has a path other than a singular circular path in a section between the central joint plane (E1) and the connection side.

Abstract: A universal joint assembly includes an assembly housing, an assembly cap coupled to the assembly housing, a rotatable mandrel, a plurality of substantially spherical drive balls, and a floating washer. The assembly housing has a plurality of pockets formed in an interior surface of the assembly housing. The rotatable mandrel is fitted within a cavity defined by the assembly housing and the assembly cap and has a plurality of pockets configured to partially receive the drive balls. The substantially spherical drive balls are rotatable within the cavity about a central axis of the mandrel. A substantially circular groove formed in the cavity is defined by a proximal end of the assembly cap and an interior wall and a shoulder of the assembly housing. The floating washer is disposed within the substantially circular groove and configured to radially displace within the groove.

Abstract: A drive power transmitting system for a rough-terrain traveling vehicle (10) includes a pair of drive shafts (177, 178) for transmitting drive power from a power unit (18) to respective right and left independently suspended rear wheels (21, 21). Right and left constant velocity joints (184, 184) are provided on respective opposed ends of the drive shafts. A bearing unit (176) is provided on each constant velocity joint for connecting the same to a final gearcase (133) provided on a vehicle body so that the left and right constant velocity joints are releasably connected to the final gearcase individually.

Abstract: In a constant velocity joint comprising an outer housing ring having an end wall with a journal and an inner surface provided with axially extending ball races and an inner ring member with outer ball races arranged in the outer housing ring and balls disposed in the ball races for the transmission of torque between the outer housing ring and the inner ring member, and a ball cage for retaining the balls in position in the ball races, a support ring is arranged in the housing ring between the end wall of the housing ring and the inner ring member for axially supporting the inner ring member during insertion of a shaft end into the inner ring member of the constant velocity joint.

Abstract: The present invention provides a steel ball rolling configuration and a constant velocity universal joint that achieve a superior oil retention effect between a surface of a steel ball and a partner rolling surface, can form a thick oil film, improve lubrication, and extend life of the steel ball. The constant velocity universal joint of the present invention includes a rolling surface and a steel ball 7 that is lubricated by grease and rolls over the rolling surface. A surface roughness of the steel ball 7 is roughened to become more similar to a surface roughness of a partner rolling surface. Numerous miniscule recesses 15 roughly tens of micrometers in size are randomly disposed on the surface of the steel ball 7.

Abstract: In a driving motor that rotates and drives a rotor by a magnetic force generated between a rotor and a stator, a constant velocity joint that transmits a rotation driving force between a driving-side rotating member and a driven-side rotating member. The driving-side rotating member and the driven-side rotating member align in an axial direction and engage with each other. The driving-side rotating member is directly connected to the rotor to function as a driving shaft.

Abstract: The rotary motion created by a motor is transmitted from the drive shaft of the motor to the driven shaft through a pair of diametrically opposed balls fitted into a coupling mechanism attached to the drive shaft and through a pin fitted into holes formed in the opposed balls and through the driven shaft disposed between the opposed balls for eliminating vibration and noise. The thrust loads imposed in the structure supporting the motor is directed to bypass the motor through a bearing supporting the driven shaft through its housing and into the outer housing surrounding the motor. The motor is encased in a cartridge disposed in a central cavity of the outer housing and the cartridge is not rigidly attached to the outer housing so that the thrust loads bypass the motor.

Abstract: The invention provides a boot for a universal joint. The boot includes a first sleeve portion defining a first circular opening. The boot also includes a second sleeve portion spaced from the first sleeve portion along a boot axis. The second sleeve portion defines a second circular opening having a smaller diameter than the first circular opening. The boot also includes a plurality of convolutions defined along the boot axis between the first sleeve portion and the second sleeve portion by a plurality of roots extending radially inward toward the boot axis and by a plurality of crests extending radially outward away from the boot axis. The plurality of roots includes a first root and a second root immediately adjacent to one another. The first root is closer to the first sleeve portion than the second root. The first root extends radially further toward the boot axis than the second root.

Abstract: A sealing sleeve (11) of the rolling boot type having a first larger, substantially cylindrical collar (12), a second smaller, substantially cylindrical collar (13), as a well as a wall portion (14) which is positioned between the collars (12, 13) and which forms at least one axially open annular fold (15) with circumferentially distributed indentations (18) in the convex curvature of the axially open annular fold (15), or with radial ribs (21) in the concave inner curvature of the axially open annular fold.

Abstract: A connecting shaft includes a fixed connecting part on one end and a connecting part on the other end for engaging with a socket, the connecting part is in curved part, a shoulder for connecting to the inner circumference of the socket is disposed between the connecting part and the connecting shaft, the purpose of the shoulder is for the connecting shaft to be able to turn or position with the socket, an axial hole is disposed inside the connecting part for a axial rod to insert into, a ball hole is disposed on each side of the connecting part and the two ball holes are connected to the axial hole, a steel ball is inserted into each ball hole, when the axial rod moves, it will also drives the two steel balls to move, one end of the axial rod is connected to a sliding control element, so that the sliding control element will drive the axial rod to move together on the axis, so as to control the two steel balls to allow the socket to turn upon the connecting shaft or to engage together in position.

Abstract: A pumping device is provided which comprises a Moineau pump with a helical rotor inside a helical cavity of a stator, driver means, and a drive connecting rod coupled by a respective coupling to a driving shaft of the driver and to one end of the rotor. Each coupling comprises a spherical head secured to the connecting rod and housed in a cavity that is cylindrical of revolution with the same diameter as and secured coaxially to the end of the rotor of the driving shaft; and a ball housed partly in a cup of the spherical head with its axis perpendicular to the axis of the connecting rod and partly in a lateral recess of the cavity.

Abstract: A constant velocity joint includes outer and inner races with mating part-spherical surfaces in which a single functional set of ball grooves are formed bearing a single torque-transmitting ball which is urged under an applied torque load toward one axial end of the joint. A retainer is carried by one of the two races or the shaft to which they are connected and acts on the ball to maintain the ball within the grooves during all angles of the joint.

Abstract: A constant velocity joint includes a first joint member having a plurality of guide rails that are parallel to one another and to a central axis of the first joint member. A second joint member includes a spider encaged by the guide rails and carrying slide couplings which are captured by but slideable axially on the guide rails and spider as well as being pivotal relative to the spider to facilitate angulation of the joint as well as axial translation during the transmission of torque between two rotatable shafts coupled to the respective first and second joint members.

Abstract: The invention relates to a constant velocity joint having an outer part 3, an inner part 8, a cage 14 and balls 24. For the purpose of fitting the inner part 8 in the cage 14, there is provided a groove 16a which can be entered by the inner part 8 by means of the web 13, so that the inner part 8 can be introduced into the cage 14, although the outer diameter of the inner part 8 is greater than that of the end aperture of the cage 14.

Abstract: A universal joint and coupling assembly is disclosed which is utilized to connect and transfer power or movement between at least two movable or moving members which respectively have different positional planes, orientations or movement axes. The invention is provided with a novel channeled spherical or ball-like guide connection member for greater angle positioning along less wearable surfacing. This guide connection member functions both to secure support attachment components which are a part of or connect to one or more moving members, and to securely allow movement through secure channeling and tracking of each of the support attachment components onto the guide connection member.

Abstract: A constant velocity joint having an inner race, an outer race provided along a periphery of the inner race, a cage sandwiched in between the inner race, the outer race, and balls. A crossing angle between a central axis of the inner race and a central axis of the outer race is bisected, and the balls are disposed within a bisection plane orthogonal to a plane including these two central axes. If a ratio tc/Da is set to rt, there is satisfied a relationship such as: (0.054/rt)·Da≦w≦(0.16/rt)·Da where Da is the major diameter of each ball, w is the circumference-directional width of each of the column members existing between the pockets adjacent to each other in the circumferential direction with respect to the cage, and tc is the diameter-directional thickness of each of the column members of the cage.

Abstract: A constant velocity joint having an inner race, an outer race provided along a periphery of the inner race, a cage sandwiched in between the inner race, the outer race, and balls. A crossing angle between a central axis of the inner race and a central axis of the outer race is bisected, and the balls are disposed within a bisection plane orthogonal to a plane including these two central axes. If a ratio tc/Da is set to rt, there is satisfied a relationship such as: (0.054/rt)·Da≦w≦(0.16/rt)·Da where Da is the major diameter of each ball, w is the circumference-directional width of each of the column members existing between the pockets adjacent to each other in the circumferential direction with respect to the cage, and tc is the diameter-directional thickness of each of the column members of the cage.

Abstract: A constant velocity joint having an inner race, an outer race provided along a periphery of the inner race, a cage sandwiched in between the inner race, the outer race, and balls. A crossing angle between a central axis of the inner race and a central axis of the outer race is bisected, and the balls are disposed within a bisection plane orthogonal to a plane including these two central axes. If a ratio tc/Da is to rt, there is satisfied a relationship such as: (0.054/rt)·Da≦w≦(0.16/rt)·Da where Da is the major diameter of each ball, w is the circumference-directional width of each of the column members existing between the pockets adjacent to each other in the circumferential direction with respect to the cage, and tc is the diameter-directional thickness of each of the column members of the cage.