Sprockets and crank assemblies

Abstract

A crank assembly for a bicycle, comprising: a chainring (302) with first teeth (708) and second teeth (714), wherein the first teeth (708) each comprise a first load flank surface (710) with a first wear resistance, and the second teeth (714) each comprise a second load flank surface (716) with a second wear resistance that is higher than the first wear resistance; and a crank arm (306) coupled to the chainring (302), wherein the second teeth (714) are arranged successively on the chainring (302) at an angle of more than 60 degrees and less than 110 degrees to a longitudinal axis of the crank arm (306) in a direction opposite to the direction of travel.

Description

BACKGROUND OF THE INVENTION1. Background AreaThis disclosure relates to bicycle drive trains, and more particularly to crank assemblies and sprockets.2. Background DescriptionA drive train of a bicycle often includes a chain operatively coupled between a crank assembly and a sprocket disposed on the rear wheel of the bicycle. The crank assembly typically uses one or more sprockets and two crank arms. During use of the bicycle, the user applies force to pedals coupled to the crank arms to rotate the sprocket. Thereby, the sprocket drives a chain that rotates the rear wheel. During operation of the sprocket, the sprocket undergoes wear.Document EP 0 008 851 A1 discloses a sprocket made of a material with low wear resistance. The sprocket has circumferential portions without teeth that are configured to receive tooth elements having at least one tooth. The tooth elements have higher wear resistance than the sprocket and replaced the missing teeth of the sprocket. As a result, the wear resistance of individual toothed segments of the sprocket wheel can be increased at the corresponding circumferential sections.SUMMARYIn one aspect, a sprocket for a crank assembly includes a first section having successive first teeth. Each of the first teeth has a first load flank surface with a first wear resistance. In addition, the sprocket includes a second section coupled to the first section. The second section has successive second teeth. Each of the second teeth has a second load flank surface with a second wear resistance that is higher than the first wear resistance. The consecutive second teeth extend over an arc length corresponding to between one twelfth and one third of a circumference of a pitch circle of the sprocket.In another aspect, a sprocket for a crank assembly includes a first tooth having a first load flank surface with a first wear resistance. In addition, the sprocket includes a second tooth having a second load flank surface with a second wear resistance that is higher than the first wear resistance. Further, the sprocket includes a third tooth disposed subsequent to the second tooth, the third tooth having a third load flank surface with the second wear resistance. The second tooth has a different thickness than the third tooth.In another aspect, a crank assembly for a bicycle includes a sprocket having first teeth and second teeth. The first teeth each have a first load flank surface with a first wear resistance. The second teeth each have a second load flank surface with a second wear resistance that is higher than the first wear resistance. The crank assembly also includes a crank arm coupled to the sprocket. The second teeth are sequentially disposed on the sprocket between more than 60 degrees and less than 110 degrees with respect to a longitudinal axis of the crank arm in a direction opposite to the direction of travel.In another aspect, a crank assembly for a bicycle includes a crank arm and only one sprocket coupled to the crank arm. The sprocket has a first tooth and a second tooth. The first tooth has a first load flank surface with a first wear resistance. The second tooth has a second load flank surface with a second wear resistance that is higher than the first wear resistance. The second tooth is to apply a maximum force to a chain with respect to the crank arm at a position on the sprocket to allow the second tooth during a maximum torque portion of a pedal revolution of the crank arm.In another aspect, a sprocket for a crank assembly includes a body having a first tooth and a second tooth. The first tooth has a first load flank surface with a first wear resistance. In addition, the sprocket includes an insert coupled to the second tooth and forming a second load flank surface of the second tooth. The second load flank surface has a second wear resistance that is higher than the first wear resistance.In another aspect, a crank assembly for a bicycle includes a first portion of a sprocket having first teeth made of a first material. In addition, the crank assembly includes a second portion of the sprocket coupled to the first portion. The second section includes second teeth made of a second material different from the first material. Further, the crank assembly includes a carrier having an arm that overlaps with the second portion of the sprocket. In addition, the crank assembly includes a first connecting member that releasably couples the first portion and the second portion to the arm of the carrier.In another aspect, a sprocket for a crank assembly includes a body having a first tooth and a second tooth, the first tooth having a first load flank surface with a first wear resistance; and an insert coupled to the second tooth and forming a second load flank surface of the second tooth, the second load flank surface having a second wear resistance that is higher than the first wear resistance. In particular, the insert does not cover the flank surface of the second tooth. Preferably, the first load flank surface of the first tooth and the body of the second tooth are of the same material, and as an optional feature, the insert is of a different material than the body.BRIEF DESCRIPTION OF THE DRAWINGSFIG. 1 is a side view of an example bicycle in which the example sprockets and crank assemblies disclosed herein may be used; FIG. 2 is a graph representative of torque outputs of a rider of the bicycle of FIG. 1 during a pedal revolution of a crank assembly; FIGS. 2A to 2C illustrate various rotational positions of the crank assembly of FIG. 2 ; FIG. 3 is a perspective view of a crank assembly as viewed from the outside; FIG. 4 is a top view of a chain that may be driven by the crank assembly of FIG. 3 ; FIG. 5 is a perspective view of a sprocket of the crank assembly of FIG. 3 viewed from the outside, engaging the chain of FIG. 4 ; FIG. 6 is a cross-sectional view of an inner link tooth that may be used with the sprocket of FIG. 5 ; FIG. 7 is a cross-sectional view of an outer link tooth that may be used with the sprocket of FIG. 5 ; FIG. 8 is a cross-sectional view of an alternative outer link tooth disclosed herein; FIG. 9 is a cross-sectional view of another alternative outer link tooth disclosed herein; FIG. 10 is an elevation of the crank assembly of FIG. 3 as viewed from the outside; FIG. 11 is a view of the sprocket of FIG. 10 viewed from the outside; FIG. 12 is another view of the sprocket of FIG. 10 viewed from the outside; FIG. 13 is another view of the sprocket of FIG. 10 viewed from the outside with two portions of the sprocket uncoupled from a body of the sprocket; FIG. 14 is a view of one of the sprocket of FIG. 13 as viewed from the inside; FIG. 15 is a perspective view of one of the portions decoupled from the sprocket of FIG. 13, as viewed from the inside; FIG. 16 is a perspective view of another embodiment of a sprocket viewed from the outside that may be used to implement any of the crank assemblies disclosed herein; FIG. 17 is a partial exploded perspective view of the sprocket of FIG. 16 as viewed from the outside; FIG. 18 is a fragmentary perspective view of the sprocket taken along the line 18--18 of FIG. 16; FIG. 19 is an elevation of yet another embodiment of a crank assembly as viewed from the outside; FIG. 20 is a cross-sectional view of a sprocket of the crank assembly of FIG. 19 taken along line 20- 20 in FIG. 19 ; FIG. 21 is a perspective view of another embodiment of a sprocket disclosed herein, viewed from the outside, that can be used to implement any of the crank assemblies disclosed herein; and FIG. 22 is a perspective view of yet another embodiment of a sprocket disclosed herein, viewed from the outside, that can be used to implement any of the crank assemblies disclosed herein.Other aspects and advantages of the embodiments disclosed herein will become apparent from the following detailed description, wherein like or similar structures bear like reference numerals.DETAILED DESCRIPTIONFIG. 1 illustrates an example bicycle 100 that may be used to implement the crank assemblies and sprockets disclosed herein. In the illustrated embodiment, the bicycle 100 includes a frame 102, a handlebar 104, and a seat 106. The bicycle 100 also includes a first wheel or front wheel 108 and a second wheel or rear wheel 110. The bicycle 100 includes a drive train 112. The drive train 112 of FIG. 1 includes a crank assembly 114, a sprocket pack or cartridge 116, and a chain 118 operatively coupling between the crank assembly 114 and the cartridge 116. The crank assembly 114 is rotatably coupled to the frame 102 and the cassette 116 is rotationally fixedly coupled to the rear wheel 110 in the direction of travel.In the illustrated embodiment, the crank assembly 114 includes a first pedal 120, a second pedal 122, a first crank arm 124, a second crank arm (see, e.g., FIG. 3 ), a carrier 126, a first sprocket 128, and a second sprocket 130. Although the example crank assembly 114 includes two sprockets (i.e., the first sprocket 128 and the second sprocket 130), other crank assemblies disclosed herein have different numbers of sprockets (e.g., 1, 3, 4, etc.). For example, the crank assembly 300 of FIG. 3 has only one sprocket.The first pedal 120 is rotatably coupled to the first crank arm 124. The second pedal 122 is rotatably coupled to the second crank arm. In the illustrated embodiment, the first crank arm 124 and the second crank arm are rotationally fixedly coupled to the carrier 126, and the carrier 126 is rotationally fixedly coupled to the first sprocket 128 and the second sprocket 130. In FIG. 1, the first sprocket 128 selectively engages the chain 118. However, the second sprocket 130 may selectively engage the chain 118. For example, the drive train 112 of FIG. 1 includes a derailleur 132 to disengage the chain 118 from the first sprocket 128 and from the second sprocket 130. The derailleur 132 may also disengage the chain 118 from the second sprocket 130 and from the first sprocket 128. A derailleur 134 moves the chain 118 between a plurality of sprockets of the cassette 116.FIG. 2 is a graph 200 representative of torque outputs of a rider of the bicycle 100 during a pedal revolution of the crank assembly 114. The graph 200 is also representative of the torque outputs of a cyclist using the crank assemblies and sprockets disclosed below with reference to FIGS. 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21-22. Accordingly, the following description of the following pedal revolution is also applicable to the crank assemblies and sprockets of FIGS. 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21-22.In the illustrated embodiment, the pedal rotation of the crank assembly 114 occurs when the rider of the bicycle 100 steps into the pedals, thereby moving the first crank arm 124 from a substantially vertical upper or first position 202 (see FIG. 2A ) 180 degrees in the direction of travel DD to a substantially vertical lower or second position 204 (see FIG. 2C ). In the illustrated embodiment, a peak or maximum torque output during the pedal revolution occurs during a maximum torque portion of the pedal revolution where the first crank arm 124 is in or near a third or horizontal position 206 (see FIG. 2B ) when the rider steps into the pedals, thereby moving the first crank arm 124 from the first position to the second position. As can be seen from FIG. 2, the maximum torque portion of the pedal revolution occurs between 60 and 100 degrees. A minimum torque output occurs during at least a portion of an initial minimum torque portion of the pedal revolution in which the first crank arm 124 is proximate to or in the first position 202 or a subsequent minimum torque portion of the pedal revolution in which the first crank arm 124 is proximate to or in the second position 204 when the rider steps into the pedals thereby moving the first crank arm 124. As used herein, the term "pedaling" means: applying, via a pedal (e.g., the first pedal 120), a force to a crank arm (e.g., the first crank arm 124 of FIG. 1 ) to rotate a sprocket (e.g., the first sprocket 128 and / or the second sprocket 130) to drive a chain (e.g., the chain 118) of a bicycle.FIGS. 3, 4-5 illustrate an embodiment of a crank assembly 300 that may be used to implement the example bicycle 100 of FIG. 1. In the illustrated embodiment, the crank assembly 300 includes only one sprocket 302. The sprocket 302 engages a chain 304 (see FIGS. 4 and 5 ). Referring to FIG. 3, the crank assembly 300 also includes a first crank arm 306 and a second crank arm 307 coupled to a carrier 308. The second crank arm 307 and the carrier 308 may be formed as a single piece or may be separate. The second crank arm 307 is schematically illustrated in FIG. 3. The carrier 308 is coupled (e.g., rotationally fixed) to the sprocket 302. The crank assembly 300 is a mirror image of the first crank arm 306.In this embodiment, the sprocket 302 includes a body 310 having a periphery 312. Sprocket 302 also includes teeth 314 disposed on the periphery 312 of body 310 for engagement with chain 304. In the illustrated embodiment, the first crank arm 306 of FIG. 3 is substantially straight or linear and has a first longitudinal axis 316. A force applied to the first crank arm 306 in a travel direction DD rotates the sprocket 302 in the travel direction about a rotational axis 317. As a result, the sprocket 302 pulls and moves the chain 304 forward across the teeth 314. The second crank arm 307 may be coupled to the carrier 308 such that a second longitudinal axis 318 of the second crank arm 307 is parallel to the longitudinal axis 316 of the first crank arm 306. In such embodiments, the sprocket 302, the first crank arm 306, and the second crank arm 307 may rotate about the axis of rotation 317.FIG. 4 is a top view of the chain 304 that may be driven by the sprocket 302 of FIG. 3. The chain 304 has a central longitudinal axis 319. The chain 304 includes outer links 320 and inner links 322. The inner links 322 are pivotally attached and coupled to the outer links 320 via bolts 324. The outer chain links 320 alternate with the inner chain links 322 in overlapping fashion.The outer links 320 have pairs of outer links 326, and the inner links 322 have pairs of inner links 328. Rollers 330 are arranged around the bolts 324. The tabs 326, 328 are provided with holes 332, and the bolts 324 extend through and protrude from the holes 332. In some embodiments, the ends 334 of the bolts 324 do not protrude from the holes 332. In the illustrated embodiment, the bolts 324 are riveted to the outer tabs 326 and the inner tabs 328. The outer links 320 overlap with the inner links 322 to define alternating outer link spaces 336 and inner link spaces 338. The outer link spaces 336 are openings defined by the outer links 326 and the rollers 330. The inner link spaces 338 are openings defined by the inner links 328 and the rollers 330.The inner link spaces 338 are rectangular. The outer link spaces 336 are "cross" or "plus sign" shaped. A first distance or width W1between a pair of opposing outer flaps 326 is greater than a second distance or width W2between a pair of opposing inner flaps 328. For example, the second widths W 2 of the inner link spaces 338 are substantially equal to a width of the rollers 330. The first widths W 1 of the outer link spaces 336 are substantially equal to the sum of the width of a roller 330 and the thickness of the second adjacent inner links 328.FIG. 5 is an enlarged perspective view of the teeth 314 of the sprocket 302 of FIG. 3 engaging the chain 304 of FIGS. 3 and 4. In the illustrated embodiment, each of the teeth 314 has one of two configurations. Each of the teeth 314 having a first configuration is referred to as outer link tooth 340 in this disclosure. Each of the teeth 314 having a second configuration is referred to as inner link tooth 342 in this disclosure. The outer link teeth 340 each have a shape and a size that match the outer link spaces 336. The outer link teeth 340 are to be received only in the outer link spaces 336 of the chain 304 during operation of the crank assembly 300. The inner link teeth 342 have a shape and size that mates with the inner link spaces 338. The inner link teeth 342 are intended to be received only in the inner link spaces 338 of the chain 304 during operation of the crank assembly 300. Therefore, in the illustrated embodiment, along the periphery 312 of the sprocket 302, the outer link teeth 340 alternate with the inner link teeth 342. When the chain 304 is engaged with the sprocket 302, the rollers 300 of the chain 304 that contact the teeth 314 are on a pitch circle 344 of the sprocket 302. Each of the outer link teeth 340 has a first tooth tip 346. Each of the inner link teeth 342 has a second tooth tip 348. In the embodiment of FIG. 5, the first tooth tips 346 each have a greater thickness than the second tooth tips 348.FIG. 6 is a cross-sectional view of one of the inner link teeth 342 ("an inner link tooth 342") taken along line 6- 6 in FIG. 5 and lying in a plane tangent to the pitch circle 344 of the sprocket 302 and extending through a center 350 of the inner link tooth 342. The inner link teeth 342 are substantially similar or the same as each other. Therefore, the following description of the inner link tooth 342 of FIG. 6 applies to each of the other inner link teeth 342 of the sprocket 302. Therefore, to avoid redundancy, the remaining inner link teeth 342 will not be separately described herein.As shown in FIG. 6, the inner link tooth 342 has a rectangular cross-sectional shape. The inner link tooth 342 has a length LT 1 in the longitudinal direction. In the illustrated embodiment, the rectangular cross-sectional shape and a first tooth width WO 1 of the inner link tooth 342 substantially match the rectangular shape and the second width W 2 of each of the inner link spaces 338 of the chain 304. For example, the inner link tooth 342 may fill or occupy one of the inner link spaces 338 over about 75% of the second width W 2 when the inner link tooth 342 is fully received within the inner link space 338. In some embodiments, the inner link tooth 342 may fill or occupy over about 80% of the second width W 2 of one of the inner link spaces 338 when the inner link tooth 342 is fully received in the inner link space 338. In some embodiments, the inner link tooth 342 may fill or occupy one of the inner link spaces 338 over about 85% of the second width W 2 when the inner link tooth 342 is fully received in the inner link space 338. In some embodiments, the inner link tooth 342 may fill or occupy different portions of the second width W 2 of one of the inner link spaces 338 when the inner link tooth 342 is fully received in the inner link space 338.FIG. 7 is a cross-sectional view of an outer link tooth 400 that may be used to realize one or more of the outer link teeth 340 of FIGS. 3 and 5. The cross-sectional view of FIG. 7 is taken along line 7- 7 in FIG. 5, which lies in a plane tangent to the pitch circle 344 of the sprocket 302 and extends through a center 402 of the outer link tooth 400. The outer link tooth 400 has a second length LT 2 in the longitudinal direction. In the illustrated embodiment, the second length LT 2, longitudinally, of the outer link tooth 400 is substantially the same as the first length LT 1, longitudinally, of the inner link tooth 342 of FIG. 6 In other embodiments, the second length LT 2, longitudinally, of the outer link tooth 400 is different than the first length LT 1, longitudinally, of the inner link tooth 342.The outer link tooth 400 of FIG. 7 includes a body 404 and an outwardly projecting protrusion 406 extending from an outer surface 408 of the body 404. The body 404 of the outer link tooth 400 of FIG. 7 does not have a protrusion extending from an inner side 410 of the body 404. The outwardly projecting protrusion 406 facilitates engagement between the outer link tooth 400 and the chain 304. In the illustrated embodiment, the outer link tooth 400 of FIG. 7 has a second tooth width WO 2 that is greater than the first tooth width WO 1. In the illustrated embodiment, the body 404 of the outer link tooth 400 has the first tooth width WO 1 and the outward protrusion 406 has a first protrusion width WP 1.As a result, the outer link tooth 400 may fill or occupy one of the outer link spaces 336 over about 75% of the first width W 1 when the outer link tooth 400 is fully received within the outer link space 336. In some embodiments, the outer link tooth 400 may fill or occupy other portions (e.g., greater than 80%, greater than 85%, etc.) of the first width W 1 of one of the outer link spaces 336 when the outer link tooth 400 is fully received within the outer link space 336.FIG. 8 is a cross-sectional view of another example outer link tooth 500 that may be used to realize one or more of the outer link teeth 340 of FIGS. 3 and 5. The cross-sectional view of FIG. 8 is taken along line 7- 7 in FIG. 5, which lies in a plane tangent to the pitch circle 344 of the sprocket 302 and extends through a center 502 of the outer link tooth 500. The outer link tooth 500 has the second length LT 2 in the longitudinal direction. In the illustrated embodiment, the second length LT 2, longitudinally, of the outer link tooth 500 is substantially the same as the first length LT 1, longitudinally, of the inner link tooth 342 of FIG. 6 In other embodiments, the second length LT 2, longitudinally, of the outer link tooth 500 is different than the first length LT 1, longitudinally, of the inner link tooth 342.The outer link tooth 500 of FIG. 8 includes a body 504 and an outwardly projecting protrusion 506 extending from an outer side 508 of the body 504. The body 504 of the outer link tooth 500 of FIG. 8 also includes an inwardly projecting protrusion 510 that extends from an inner side 512 of the body 504. The outward protrusion 506 and the inward protrusion 510 facilitate the engagement between the outer link tooth 500 and the chain 304. In the illustrated embodiment, the outer link tooth 500 of FIG. 8 has a third tooth width WO 3 that is greater than the first tooth width WO 1. In some embodiments, the third tooth width WO 3 is greater than the second tooth WO 2. In the illustrated embodiment, the outward protrusion 506 has the first protrusion width WP 1 and the inward protrusion 510 has a second protrusion width WP 2 that is less than the first protrusion width WP 1.As a result, the outer link tooth 500 may fill or occupy one of the outer link spaces 336 over about 75% of the first width W 1 when the outer link tooth 500 is fully received within the outer link space 336. In some embodiments, the outer link tooth 500 may fill or occupy other portions (e.g., greater than 80%, greater than 85%, etc.) of the first width W 1 of one of the outer link spaces 336 when the outer link tooth 500 is fully received within the outer link space 336.FIG. 9 is a cross-sectional view of another example outer link tooth 600 that may be used to realize one or more of the outer link teeth 340 of FIGS. 3 and 5. The cross-sectional view of FIG. 9 is taken along line 7- 7 in FIG. 5, which lies in a plane tangent to the pitch circle 344 of the sprocket 302 and extends through a center 602 of the outer link tooth 600. The outer link tooth 600 has the second length LT 2 in the longitudinal direction. In the illustrated embodiment, the second length LT 2, longitudinally, of the outer link tooth 600 is substantially the same as the first length LT 1, longitudinally, of the inner link tooth 342 of FIG. 6 In other embodiments, the second length LT 2, longitudinally, of the outer link tooth 600 is different than the first length LT 1, longitudinally, of the inner link tooth 342.The outer link tooth 600 of FIG. 9 includes a body 604 and an outwardly projecting protrusion 606 extending from an outer surface 608 of the body 604. The body 604 of the outer link tooth 600 of FIG. 9 also includes an inwardly projecting protrusion 610 that extends from an inner side 612 of the body 604. The outward protrusion 606 and the inward protrusion 610 facilitate the engagement between the outer link tooth 600 and the chain 304. In the illustrated embodiment, the outer link tooth 600 of FIG. 9 has a fourth tooth width WO 4 that is greater than the first tooth width WO 1. In some embodiments, the fourth tooth width WO 4 is greater than the second tooth width WO 2. In other embodiments, the fourth tooth width WO 4 is greater than the third tooth WO 3. In the illustrated embodiment, the outward protrusion 606 has the first protrusion width WP 1 and the inward protrusion 610 has a first protrusion width WP 1.As a result, the outer link tooth 600 may fill or occupy one of the outer link spaces 336 over about 75% of the first width W 1 when the outer link tooth 600 is fully received within the outer link space 336. In some embodiments, the outer link tooth 600 may fill or occupy other portions (e.g., greater than 80%, greater than 85%, etc.) of the first width W 1 of one of the outer link spaces 336 when the outer link tooth 600 is fully received within the outer link space 336.FIG. 10 shows the crank assembly 300 in the second or horizontal position. Thus, the longitudinal axis 316 of the first crank arm 306 of FIG. 3 is horizontal as shown in FIG. 10. In the illustrated embodiment, the sprocket 302 includes a first portion 700, a second portion 702, a third portion 704, and a fourth portion 706. In the illustrated embodiment, the first portion 700 and the fourth portion 706 are formed as a unit and / or integral with the body 310 of the sprocket 302. For example, the first section 700, the fourth section 706, and the body 310 may be formed of an aluminum alloy by stamping from one piece. In the illustrated embodiment, the first portion 700 includes a predetermined number of teeth 314. For example, the first section 700 of FIG. 10 includes nine of the teeth 314. In other embodiments, the first portion 700 includes different numbers of teeth 314 (e.g., 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, etc.). The teeth 314 of the first section 700 are referred to herein as first teeth 708.The first teeth 708 are arranged in sequence on the first section 700. Thus, the first teeth 708 are the outer link teeth 340 and the inner link teeth 342 alternating with the outer link teeth 340. Consequently, successive teeth of the first teeth 708 have different thicknesses. For example, a first of the first teeth 708 may be an inner link tooth 342 having a first tooth width WO 1, and a second of the first teeth 708 disposed subsequent to the first of the first teeth 708 may have the fourth tooth width WO 4 that is greater than the first tooth width WO 1.In the illustrated embodiment, the first teeth 708, and more specifically, a first load flank surface 710 of each of the first teeth 708 has a first wear resistance. A load flank surface as used in this disclosure is a surface of a tooth (e.g., one of the teeth 314) that contacts a roller (e.g., the rollers 330) of a chain and applies force to the chain to drive the chain. In some embodiments, the first load flank surfaces 710 of the first teeth 708 have a first flatness, a first hardness, a wear protection layer, and / or one or more further and / or alternative features that enable the first teeth 708 to have the first wear resistance. In the illustrated embodiment, the first teeth 708, including the first load flank surfaces 710, are made of heat-treated wrought aluminum alloy. In other embodiments, the first teeth 708 and / or the first load flank surfaces 710 are made of other materials.The second section 702 is coupled to the body 310 of the sprocket 302. In the illustrated embodiment, the second portion 702 includes a first carrier 712 permanently coupled to the body 310 of the sprocket 302. For example, the first beam 712 may be permanently coupled to the body 310 by welding, brazing, bonding, and / or one or more additional and / or alternative fasteners. As used herein, the term "permanently coupled" has the meaning: coupled in a manner that is intentionally difficult to release and / or cannot be intentionally uncoupled without damaging or destroying one or more components. In other embodiments, the first carrier 712 is releasably coupled to the body 310 of the sprocket 302. For example, one or more bolts and / or one or more additional and / or alternative fasteners may releasably couple the first carrier 712 to the body 310 of the sprocket 302. As used in this disclosure, the term "releasably coupled" means: coupled in a manner that is intentionally releasable.The second section 702 has a predetermined number of teeth 314. In the illustrated embodiment, the second section 702 includes eight of the teeth 314. In other embodiments, the second section 702 includes different numbers of teeth 314 (e.g., 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, etc.). In the illustrated embodiment, the second section 702 has a different number of teeth 314 than the first section 700. In other embodiments, the second section 702 has the same number of teeth 314 as the first section 700. The teeth 314 of the second section 702 are referred to herein as second teeth 714. In the illustrated embodiment, the second teeth 714 are formed as a unit and / or integral with the first carrier 712. In other embodiments, the second teeth 714 are coupled to the first carrier 712.The second teeth 714 are arranged in succession on the second section 702. Thus, the second teeth 714 are the outer link teeth 340 and the inner link teeth 342 alternating with the outer link teeth 340. Consequently, successive teeth of the second teeth 714 have different thicknesses. For example, a first of the second teeth 714 may be an inner link tooth 342 having a first tooth width WO 1 and a second of the second teeth 314 disposed subsequent to the first of the second teeth 714 may have the fourth tooth width WO 4 that is greater than the first tooth width WO 1.In the illustrated embodiment, the second teeth 714, and more specifically, a second load flank surface 716 of each of the second teeth 714 has a second wear resistance that is higher than the first wear resistance. In some embodiments, the second load flank surfaces 716 of the second teeth 714 have a second flatness, more planar than the first flatness, a second hardness, more severe than the first hardness, a wear protection layer, and / or one or more further and / or alternative features that allow the second teeth 714 to have the second wear resistance. In the illustrated embodiment, the second teeth 714, including the second load flank surfaces 716, are of alloyed mild steel. In some embodiments, the second teeth 714, including the second load flank surfaces 716, are made of a titanium alloy. In other embodiments, the second teeth 714 and / or the second load flank surfaces 716 are made of other materials. The second teeth may be four times more wear resistant than the first teeth.The third portion 704 is also permanently coupled to the body 310 of the sprocket 302. In the illustrated embodiment, the third portion 704 includes a second carrier 718 that is permanently coupled to the body 310 of the sprocket 302. For example, the second beam 718 may be permanently coupled to the body 310 by welding, brazing, bonding, and / or one or more additional and / or alternative fasteners. In other embodiments, the second carrier 718 is releasably coupled to the body 310 of the sprocket 302. For example, one or more bolts and / or one or more additional and / or alternative fasteners may releasably couple the second carrier 718 to the body 310 of the sprocket 302.The third section 704 includes a predetermined number of teeth 314. In the illustrated embodiment, the third portion 704 includes eight of the teeth 314. Thus, in the illustrated embodiment, the second portion 702 and the third portion 704 have the same number of teeth. In other embodiments, the third portion 704 includes different numbers of teeth 314 (e.g., 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, etc.). In some embodiments, the third portion 704 has a different number of teeth 314 than the second portion 702. The teeth 314 of the third section 704 are referred to herein as third teeth 720. In the illustrated embodiment, the third teeth 720 are formed as a unit and / or integral with the second carrier 718. In other embodiments, the third teeth 720 are coupled to the second carrier 718.The third teeth 720 are arranged consecutively on the third section 704. Thus, the third teeth 720 are the outer link teeth 340 and the inner link teeth 342 alternating with the outer link teeth 340. Consequently, successive teeth of the third teeth 720 have different thicknesses. For example, a first of the third teeth 720 may be an inner link tooth 342 having a first tooth width WO 1, and a second of the third teeth 720 disposed subsequent to the first of the third teeth 720 may have the fourth tooth width WO 4 that is greater than the first tooth width WO 1.In the illustrated embodiment, the third teeth 720, and more specifically, a third load flank surface 722 of each of the third teeth 720, have a third wear resistance that is higher than the first wear resistance. In some embodiments, the third wear resistance is higher than the second wear resistance. In other embodiments, the third wear resistance is less than the second wear resistance. In still further embodiments, the third wear resistance is equal to the second wear resistance. In some embodiments, the third load flank surfaces 722 of the third teeth 720 have a third flatness more planar than the first flatness, a third hardness harder than the first hardness, a wear protection layer, and / or one or more further and / or alternative features that allow the third teeth 720 to have the third wear resistance. In the illustrated embodiment, the third teeth 720, including the third load flank surfaces 722, are of alloyed mild steel. In some embodiments, the third teeth 720, including the third load flank surfaces 722, are made of a titanium alloy. In other embodiments, the third teeth 720 and / or the third load flank surfaces 722 are made of other materials.In the illustrated embodiment, the fourth portion 706 includes a predetermined number of teeth 314. For example, the fourth portion 706 of FIG. 10 includes nine of the teeth 314. In other embodiments, the fourth portion 706 includes different numbers of teeth 314 (e.g., 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, etc.). The teeth 314 of the fourth section 706 are referred to herein as fourth teeth 724.The fourth teeth 724 are arranged in succession on the fourth section 706. Thus, the fourth teeth 724 are the outer link teeth 340 and the inner link teeth 342 alternating with the outer link teeth 340. Consequently, successive teeth of the fourth teeth 724 have different thicknesses. For example, a first of the fourth teeth 724 may be an inner link tooth 342 having a first tooth width WO 1 and a second of the fourth teeth 724 disposed subsequent to the first of the fourth teeth 724 may have the fourth tooth width WO 4 that is greater than the first tooth width WO 1.In the illustrated embodiment, the fourth teeth 724, and more specifically, a fourth load flank surface 726 of each of the fourth teeth 724 has a first wear resistance. In some embodiments, the fourth load flank surfaces 726 of the fourth teeth 724 have the first flatness, the first hardness, and / or one or more further and / or alternative features that enable the fourth teeth 724 to have the first wear resistance. In the illustrated embodiment, the fourth teeth 724, including the fourth load flank surfaces 726, are made of heat-treated wrought aluminum alloy. In other embodiments, the fourth teeth 724 are of different materials.FIG. 11 is a front view of the sprocket 302 of FIG. 3 uncoupled from the carrier 308 and the first crank arm 306. However, the longitudinal axis 316 of the first crank arm 306 is shown in FIG. 11. As discussed above with respect to FIG. 2, when the rider steps into the pedals and thereby moves the first crank arm 306, the peak or maximum torque output during a pedal revolution using the crank assembly 300 of FIG. 3 occurs during a maximum torque portion of the pedal revolution in which the longitudinal axis 316 of the first crank arm 306 is horizontal or nearly horizontal. As a result, at least one of the teeth 314 that engage and advance the chain 304 applies a maximum force to the chain 304 during the maximum torque portion of the pedal revolution.In this disclosure, a tooth on a sprocket is disposed "behind" a longitudinal axis of a crank arm at an angle measured from the longitudinal axis of the first crank arm 306 in a direction opposite to the direction of travel, the angle having an apex at the intersection of the longitudinal axis of the crank arm and a rotational axis (e.g., the rotational axis 317 of FIG. 11 ) of the sprocket 302. In this disclosure, a tooth on a sprocket is disposed "forward of" a longitudinal axis of a crank arm at an angle measured from the longitudinal axis of the crank arm in the direction of travel, the angle having an apex at the intersection of the longitudinal axis of the crank arm and the rotational axis of the sprocket.In the present disclosure, the following terms are used: a tooth that is between more than zero degrees and 180 degrees or less behind a longitudinal axis of a crank arm with respect to the direction of travel is referred to herein as "following" the longitudinal axis of the crank arm. A tooth that is more than 180 degrees and less than 360 degrees behind the longitudinal axis of the crank arm with respect to the direction of travel is referred to herein as "preceding" the longitudinal axis of the crank arm.As discussed above with respect to FIG. 2, during a pedal revolution of the crank assembly 300 of FIGS. 10 and 11, the first crank arm 306 moves from the first position 202, FIG. 2A ) to the third position 204 (FIG. 2C ). As a result, during the pedal revolution of the first crank arm 306, the first teeth 708 of the first section 700, the second teeth 714 of the second section 702, and the fourth teeth 724 of the fourth section 706 sequentially engage the chain 304. The second teeth 714 are disposed on the sprocket 302 to engage the chain 304 and apply a maximum force to the chain 304 when the first crank arm 306 is in or near the third position 206 (FIG. 2B ). Thus, in the illustrated embodiment, the second teeth 714 of the second portion 702 of the sprocket 302 are at positions on the sprocket 302 relative to the first crank arm 306 that allow at least one of the second teeth 714 to engage the chain 304 and apply the maximum force to the chain 304 during the maximum torque portion of the pedal revolution of the first crank arm 306. For example, in the embodiment of FIG. 11, the second teeth 714 on the sprocket 302 are arranged in sequence between about an angle X and about an angle Y behind the longitudinal axis 316 of the first crank arm 306 with respect to the direction of travel DD. In the illustrated embodiment, the angle X is about 85 degrees and the angle Y is about 155 degrees. In other embodiments, the second teeth 714 on the sprocket 302 are disposed behind the longitudinal axis 316 of the first crank arm 306 with respect to the direction of travel DD at different degrees, such as between greater than 60 degrees and less than 180 degrees, between 30 degrees and 210 degrees, between 60 degrees and 90 degrees, and / or at different degrees. As mentioned above, the second teeth 714 on the sprocket 302 are arranged in succession between about 85 degrees and about 155 degrees behind the longitudinal axis 316 of the first crank arm 306 with respect to the direction of travel DD. Thus, the second teeth 714 extend over an arc length corresponding to about 7 / 36 of a perimeter of the pitch circle 344 of the sprocket 302 as measured from the contact point 728 of an initial one of the second teeth 714 to the contact point 728 of a last one of the second teeth 714 with respect to the travel direction DD. In other embodiments, the second teeth 714 extend over different arc lengths. For example, the second teeth 714 may extend over arc lengths corresponding to between a twelfth and a third of a perimeter of the pitch circle 344 of the sprocket 302.FIG. 12 is a similar view of the sprocket 302 shown in FIG. 11. The first teeth 708 of FIG. 11 are at positions on the sprocket 302 that allow the first teeth 708 to engage the chain 204 and exert a minimum force on the chain 304 when the first crank arm 306 is in or near the first position 202 (FIG. 2A ). Thus, in the present embodiment, the first teeth 708 of the first portion 700 are at positions on the sprocket 302 relative to the first crank arm 306 that allow at least one of the first teeth 708 to engage the chain 304 and exert a minimum force on the chain 304 during the initial minimum torque portion of the pedal revolution of the first crank arm 306. For example, the first teeth 708 on the sprocket 302 are arranged in sequence between about an angle A forward of the longitudinal axis 316 and about an angle B rearward of the longitudinal axis 316 of the first crank arm 306 with respect to the direction of travel DD. In the illustrated embodiment, the angle A is about 12 degrees and the angle B is about 73 degrees. In other embodiments, the first teeth 708 are at different positions relative to the first crank arm 306. Consequently, the first teeth 708 extend over an arc length corresponding to about 3 / 14 of the perimeter of the pitch circle 344 of the sprocket 302 as measured from the contact point 728 of an initial one of the first teeth 710 to the contact point 728 of a last one of the first teeth 708 with respect to the travel direction DD. In other embodiments, the first teeth 710 extend over different arc lengths.In the embodiment of FIG. 12, the fourth portion 706 is a mirror image of the first portion 700 and is diametrically opposed to the first portion 700. As a result, the fourth teeth 724 are at positions on the sprocket 302 that allow the fourth teeth 724 to exert the minimum force when the first crank arm 306 moves through the third or horizontal position 206 (FIG. 2B ) and to the second position 204 (FIG. 2C ). Thus, in the illustrated embodiment, the fourth teeth 724 of the fourth section 706 are at positions on the sprocket 302 relative to the first crank arm 306 that allow at least one of the fourth teeth 724 to engage the chain 304 and apply the minimum force to the chain 304 during the subsequent minimum torque portion of the pedal revolution of the first crank arm 306.During a pedal revolution of the second crank arm 307 of the crank assembly 300, the second crank arm 307 moves from the first position 202 (FIG. 2A ) to the third position 204 (FIG. 2C ). As a result, during the pedal revolution, the fourth teeth 724 of the fourth section 706, the third teeth 720 of the third section 704, and the first teeth 708 of the first section 700 sequentially engage the chain 304. In the illustrated embodiment, the third portion 704 is a mirror image of the second portion 702, the first portion 700 is a mirror image of the fourth portion 706, and the second crank arm 307 is a mirror image of the first crank arm 306. Further, the third section 704 is diametrically opposed to the second section 702. Therefore, the above description of the positions of the second teeth 714 relative to the first crank arm 306 applies to the positions of the third teeth 720 relative to the second crank arm 307. As a result, during the pedal revolution of the second crank arm 307, the fourth teeth 724 engage the chain 304 and exert a minimum force on the chain 304 during the initial minimum torque portion of the pedal revolution of the second crank arm 307; the third teeth 720 engage the chain 304 and exert the maximum force on the chain 304 during the maximum torque portion of the pedal revolution of the second crank arm 307; and the first teeth engage the chain 304 and exert a minimum force on the chain 304 during the subsequent minimum torque portion of the pedal revolution of the second crank arm 307.Turning now to FIG. 13, the outer surface 730 of the sprocket 302 is shown with the second portion 702 and the third portion 704 uncoupled from the body 310. In the illustrated embodiment, the periphery 312 of the body 310 of the sprocket 302 includes a first peripheral portion 732, a second peripheral portion 734, a third peripheral portion 736, and a fourth peripheral portion 738. The first peripheral portion 732 is integral and / or unitary with the first teeth 710, and the fourth peripheral portion 738 is integral and / or unitary with the fourth teeth 724.The second peripheral portion 734 of FIG. 12 has no teeth. In the illustrated embodiment, the second peripheral portion 734 includes a first seating region 740 on the outer surface 730 of the sprocket 302 to receive the first carrier 712 (see FIG. 10 ). Referring to the embodiment of FIG. 12, the first seating portion 740 is a recess having a size and shape that matches a size and shape of the first carrier 712. The third peripheral portion 736 also has no teeth. In the illustrated embodiment, the third peripheral portion 736 includes a second seating region 742 to receive the second carrier 718 (see FIG. 10 ). In the illustrated embodiment, the second seating region 742 is a recess having a size and shape that matches the size and shape of the second carrier 718. In other embodiments, the first seating area 740 and / or the second seating area 742 are implemented in another manner.FIG. 14 illustrates the inner side 744 of the sprocket 302 with the second section 702 and the third section 704 uncoupled from the body 310. In the illustrated embodiment, the second circumferential portion 734 and the third circumferential portion 736 do not include seating areas for the first carrier 712 and the second carrier 718, respectively, on the inner side 744 of the sprocket 302. In other embodiments, the second perimeter portion 734 and / or the third perimeter portion 736 include seating areas (e.g., recesses) to receive portions of the first carrier 712 and / or the second carrier 718, respectively.FIG. 15 is a perspective view of an embodiment of the second portion 702 of the sprocket 302. In the illustrated embodiment, the first carrier 712 includes an arcuate flange 746. When the second section 702 is coupled to the body 310 of the sprocket 302, the flange 746 is received in the first seating region 740 of the second circumferential portion 734 of the body 310. Portions of the second teeth 714 extend or protrude from the flange 746 and form a cantilevered undersurface 748. When the second portion 702 is coupled to the body 310, the bottom surface 748 seats on and / or is supported by the perimeter 312 of the body 310, and an inwardly facing side 750 of the flange 746 abuts the first seating region 740. In the present embodiment of the sprocket 302, the third portion 704 is substantially similar or the same as the second portion 702 of FIG. 15. Accordingly, the above description of the second section 702 applies to the third section 704. Therefore, to avoid redundancy, the third portion 704 of the sprocket 302 is not separately described herein.FIG. 16 is another embodiment of a sprocket 800 disclosed herein that may be used to implement the crank assembly 112 of FIG. 1 and / or the crank assembly 300 of FIG. 3. In the illustrated embodiment, the sprocket 800 includes a first portion 802, a second portion 804, a third portion 806, and a fourth portion 808. In the illustrated embodiment, the first portion 802 is a mirror image of the fourth portion 808 and the first portion 802 is diametrically opposed to the fourth portion 808. The third portion 806 is a mirror image of the second portion 804, and the third portion 806 is diametrically opposed to the second portion 804.In the illustrated embodiment, the first portion 802 includes consecutive first teeth 810 having a first wear resistance. The second portion 804 includes consecutive second teeth 812 having a second wear resistance that is greater than the first wear resistance. The third section 806 has successive third teeth 814 with a third wear resistance. In some embodiments, the third wear resistance is substantially equal to the second wear resistance. In some embodiments, the third wear resistance is less than or greater than the second wear resistance. The fourth section 808 has consecutive fourth teeth 816 with the first wear resistance.In the illustrated embodiment, the first teeth 810, the second teeth 812, the third teeth 814, and the fourth teeth 816 are substantially the same size and shape. For example, the first teeth 810, the second teeth 812, the third teeth 814, and the fourth teeth 816 have substantially the same thickness. In the illustrated embodiment, the first portion 802 and the fourth portion 808 are integral and / or unitary with a body 818 of the sprocket 800. The second section 804 is coupled to the body 818 via three first connectors 820. The third section 806 is also coupled to the body 818 via three second connectors 822. In other embodiments, the second portion 804 and / or the third portion 806 are coupled to the body 818 via other numbers of fasteners (e.g., 1, 2, 4, 5, etc.).When a crank arm (e.g., crank arm 124 of FIG. 1, first crank arm 306 of FIG. 3, and / or second crank arm 307 of FIG. 3 ) is coupled to sprocket 800 of FIG. 16, second teeth 812 of second section 804 and / or third teeth 814 of third section 806 are engaged with a chain (e.g., chain 304) at positions on sprocket 800 relative to the crank arm that allow at least one of second teeth 812 and / or third teeth 814 to exert a maximum force on the chain during the maximum torque portion of the pedal revolution of sprocket 800. The first teeth 810 of the first portion 802 are at positions on the sprocket 302 relative to the crank arm that allow at least one of the first teeth 810 to engage the chain and exert a minimum force on the chain 304 during an initial portion of minimum torque of pedal rotation of the sprocket 800. The fourth teeth 816 of the fourth section 808 are at positions on the sprocket 800 relative to the crank arm that allow at least one of the fourth teeth 816 to engage the chain and exert the minimum force on the chain 800 during the subsequent minimum torque portion of the pedal rotation of the sprocket.FIG. 17 is an exploded view of the sprocket 800 of FIG. 8. In the illustrated embodiment, the body 818 of the sprocket 800 includes a circumferential portion 824 that has no teeth. The peripheral portion 824 of the sprocket 800 supports the second section 804. In the illustrated embodiment, the peripheral portion 824 does not include a recess for receiving the second section 804.FIG. 18 is a cross-sectional view of the body 818 and the second section 804 taken along line 17-17 in FIG. 16. FIG. 18 illustrates the second section 804 resting on the perimeter portion 824 of the body 818. In the illustrated embodiment, the second section 804 includes an L-shaped beam 826 that rests on the perimeter portion 826. In other embodiments, the carrier 826 is shaped differently. For example, the carrier 826 may be U-shaped.FIG. 19 shows another embodiment of a crank assembly 900. In the illustrated embodiment, the crank assembly 900 includes a sprocket 902, a carrier 904, a first crank arm 906, and a second crank arm 908. The first crank arm 906, the second crank arm 908, and the sprocket 902 rotate about an axis of rotation 910 during a pedal revolution of the crank assembly 900. According to the perspective of Fig. 19, the pivot axis 910 extends into the sheet. The first crank arm 906 has a first longitudinal axis 912 that intersects the rotational axis 910. The second crank arm 906 has a second longitudinal axis 914 that is parallel to the first longitudinal axis 912 and intersects the rotational axis 910.In the illustrated embodiment, the carrier 904 includes a first arm 916, a second arm 918, a third arm 920, and a fourth arm 922. In other embodiments, the carrier 904 has other numbers of arms (e.g., 1, 2, 3, 5, 6, etc.). In the illustrated embodiment, the first arm 916, the second arm 918, the third arm 920, and the fourth arm 922 extend radially outward from a hub 924 of the carrier 904. The first crank arm 906 and the second crank arm 908 are rotationally fixedly coupled to the hub 924 of the carrier 904.The sprocket 902 includes a first portion or bridge member 926, a second portion or bridge member 928, a third portion or bridge member 930, and a fourth portion or bridge member 932. In the illustrated embodiment, the first bridge member 926 has consecutive first teeth 934, the second bridge member 928 has consecutive second teeth 936, the third bridge member 928 has consecutive third teeth 938, and the fourth bridge member 930 has consecutive fourth teeth 940. In some embodiments, the first teeth 934, the second teeth 936, the third teeth 938, and / or the fourth teeth 940 are alternating outer link teeth and inner link teeth that may have shapes and / or sizes similar or equal to those described herein, e.g., the outer link teeth 340 of FIG. 5, the outer link teeth 400 of FIG. 7, the outer link teeth 500 of FIG. 8, the outer link teeth 600 of FIG. 9, and / or the inner link teeth 342 of FIGS. 5 and 6.In the illustrated embodiment, the first bridge member 926 extends across a first space 942 between the first arm 916 of the carrier 904 and the second arm 918 of the carrier 904. The second bridge member 928 extends over or bridges a second space 944 between the second arm 918 and the third arm 920. The third bridge member 930 bridges a third space 946 between the first arm 916 and the fourth arm 922. The fourth bridge member 932 extends across a fourth space 948 between the third arm 920 and the fourth arm 922.A first connecting member 950 releasably couples the first bridge member 926 and the second bridge member 928 to the second arm 918 of the carrier 904. A second link 952 releasably couples the first bridge member 926 and the third bridge member 930 to the first arm 916 of the carrier 904. A third link 954 releasably couples the second bridge 928 and the fourth bridge 932 to the third arm 920 of the bracket 904. A fourth link 956 detachably couples the third bridge element 930 and the fourth bridge element 932 to the fourth arm 922 of the carrier 904. Thus, each of the bridge members 926, 928, 930, 932 may be individually decoupled from the crank assembly 900. As such, unlike conventional sprockets that need to be replaced in their entirety when only some teeth reach the end of their useful life, the example sprocket 902 of FIG. 19 allows for the replacement of selected ones of the bridge members 926, 928, 930, 932.In the illustrated embodiment, the first teeth 934 and, more specifically, a first load flank surface 958 of each of the first teeth 934 has a first wear resistance. In some embodiments, the first load flank surfaces 958 of the first teeth 934 have a first flatness, a first hardness, and / or one or more further and / or alternative features that enable the first teeth 934 to have the first wear resistance. In the illustrated embodiment, the first bridge member 926, including the first teeth 934, is made of heat-treated wrought aluminum alloy. In other embodiments, the first bridge member 926 and / or the first teeth 934 are of different materials.In the illustrated embodiment, the second teeth 936 and, more specifically, a second load flank surface 960 of each of the second teeth 936 has a second wear resistance that is higher than the first wear resistance. In some embodiments, the second load flank surfaces 960 of the second teeth 936 have a second flatness, more planar than the first flatness, a second hardness, more severe than the first hardness, a wear protection layer, and / or one or more further and / or alternative features that allow the second teeth 936 to have the second wear resistance. In the illustrated embodiment, the second bridge member 928 including the second teeth 936 is made of alloyed mild steel. In some embodiments, the second bridge member 928 including the second teeth 936 is made of a titanium alloy. In other embodiments, the second bridge member 928 and / or the second teeth 936 are of different materials.In the illustrated embodiment, the third teeth 938, and more specifically, a third load flank surface 962 of each of the third teeth 938 have a third wear resistance that is higher than the first wear resistance. In some embodiments, the third wear resistance is higher than the second wear resistance. In other embodiments, the third wear resistance is less than the second wear resistance. In still further embodiments, the third wear resistance is equal to the second wear resistance. In some embodiments, the third load flank surfaces 962 of the third teeth 938 have a third flatness, more planar than the first flatness, a third hardness, more severe than the first hardness, a wear protection layer, and / or one or more further and / or alternative features that enable the third teeth 938 to have the third wear resistance. In the illustrated embodiment, the third bridge member 930 including the third teeth 938 is made of alloyed mild steel. In some embodiments, the third teeth 938 including the third load flank surfaces 962 are made of a titanium alloy. In other embodiments, the third bridge member 930 and / or the third teeth 938 are of different materials.In the illustrated embodiment, the fourth teeth 940 and, more specifically, a fourth load flank surface 964 of each of the fourth teeth 940 has a fourth wear resistance. In some embodiments, the fourth load flank surfaces 964 of the fourth teeth 940 include the fourth flatness, hardness, and / or one or more other and / or alternative features that enable the fourth teeth 940 to have the fourth wear resistance. In some embodiments, the fourth wear resistance is equal to the first wear resistance. In further embodiments, the fourth wear resistance is greater or less than the first wear resistance. In the illustrated embodiment, the fourth bridge member 932, including the fourth teeth 740, is made of heat-treated wrought aluminum alloy. In other embodiments, the fourth bridge element 932 is made of other materials.In the illustrated embodiment, the second teeth 936 of the second bridge member 928 are at positions on the sprocket 902 relative to the first crank arm 906 that allow at least one of the second teeth 936 to engage a chain (e.g., the chain 304) and apply a maximum force to the chain during the maximum torque portion of a pedal revolution of the first crank arm 906. For example, the second teeth 936 on the sprocket 902 may be arranged in sequence between a first predetermined angle (e.g., angle 1 of FIG. 19 ) and a second predetermined angle (e.g., angle 2 of FIG. 19 ) behind the first longitudinal axis 912 of the first crank arm 906 with respect to the direction of travel DD. For example, the second teeth 936 on the sprocket 902 may be arranged between about 45 degrees and about 130 degrees behind the first longitudinal axis 912 of the first crank arm 906 in sequence with respect to the direction of travel DD. In other embodiments, the second teeth 936 on the sprocket 902 are disposed behind the longitudinal axis 912 of the first crank arm 906 with respect to the direction of travel DD at other degrees, such as between greater than 60 degrees and less than 180 degrees, between 30 degrees and 210 degrees, between 60 degrees and 90 degrees, and / or at other degrees.The third teeth 938 of the third bridge member 930 are at positions on the sprocket 902 relative to the second crank arm 908 that allow at least one of the second teeth 938 to engage the chain and apply a maximum force to the chain during the maximum torque portion of a pedal revolution of the second crank arm 908. For example, the third teeth 938 on the sprocket 902 may be arranged in sequence between a third predetermined angle (e.g., the angle 3 of FIG. 19 ) and a fourth predetermined angle (e.g., the angle 4 of FIG. 19 ) behind the second longitudinal axis 914 of the second crank arm 908 with respect to the travel direction DD. In some embodiments, the third predetermined angle and / or the fourth predetermined angle are equal to the first predetermined angle and the second predetermined angle, respectively. In other embodiments, the third predetermined angle and / or the fourth predetermined angle are different from the first predetermined angle and the second predetermined angle, respectively.The first teeth 934 of the first bridge member 926 are at positions on the sprocket 902 relative to the first crank arm 906 that allow at least one of the first teeth 934 to engage the chain and exert a minimum force on the chain during an initial portion of minimum torque of the pedal rotation of the first crank arm 906. Further, the first teeth 934 of the first bridge member 926 are at positions on the sprocket 902 relative to the second crank arm 908 that allow at least one of the first teeth 934 to engage the chain and exert a minimum force on the chain during a subsequent portion of minimum torque of the pedal rotation of the second crank arm 908. For example, the first teeth 934 on the sprocket 902 are arranged in sequence between a fifth predetermined angle (e.g., the angle 5 of FIG. 19 ) forward of the first longitudinal axis 912 of the first crank arm 906 and a sixth predetermined angle (e.g., the angle 6 of FIG. 19 ) rearward of the first longitudinal axis 712 of the first crank arm 906 with respect to the direction of travel DD. For example, the fifth predetermined angle may be about 40 degrees and the sixth predetermined angle may be about 40 degrees. In other embodiments, the first teeth 708 are at different positions relative to the first crank arm 906.The fourth teeth 940 of the fourth bridge member 932 are at positions on the sprocket 902 relative to the first crank arm 906 that allow at least one of the fourth teeth 940 to engage the chain and exert a minimum force on the chain during the subsequent minimum torque portion of the pedal rotation of the first crank arm 906. Further, the fourth teeth 940 of the fourth bridge member 932 are at positions on the sprocket 902 relative to the second crank arm 908 that allow at least one of the fourth teeth 940 to engage the chain and apply a minimum force to the chain during the subsequent minimum torque portion of the pedal rotation of the second crank arm 908. For example, the fourth teeth 940 on the sprocket 902 may be arranged in sequence between a seventh predetermined angle (e.g., the angle 7 of FIG. 19 ) forward of the second longitudinal axis 914 and an eighth predetermined angle (e.g., the angle 8 of FIG. 19 ) rearward of the second longitudinal axis 914 of the second crank arm 908 with respect to the travel direction DD. In some embodiments, the seventh predetermined angle and / or the eighth predetermined angle are equal to the fifth predetermined angle and the sixth predetermined angle, respectively. In some embodiments, the seventh predetermined angle and / or the eighth predetermined angle are different from the fifth predetermined angle and the sixth predetermined angle, respectively.FIG. 20 is a cross-sectional view of the sprocket 902 and the carrier 904 taken along line 20- 20 in FIG. 19, FIG. 20 illustrates an example linkage 966 for releasably coupling the second bridge member 928 and the fourth bridge member 932 to the third arm 920 of the carrier 904. In the illustrated embodiment, the third arm 920 overlaps the second bridge member 928 and the fourth bridge member 932 such that a first opening 968 of the second bridge member 928, a second opening 970 of the fourth bridge member 932, and a third opening 972 of the third arm 920 are substantially coaxial. The third link 954 extends through the second bridge 928, the fourth bridge 932, and the third arm 920 of the carrier 904, through the first opening 968, the second opening 970, and the third opening 972 respectively. The third connecting member 954 of FIG. 20 includes a bolt 974 and a nut 976 screwed on the bolt 974. In other embodiments, the connection 966 uses one or more other and / or alternative types of connection elements.FIG. 21 is another embodiment of a sprocket 1000 that may be used to implement any of the disclosed crank assemblies, e.g., the example crank assembly 112 of FIG. 1, the example crank assembly 300 of FIG. 3, and / or the example crank assembly 900 of FIG. 19. In the illustrated embodiment, the sprocket 1000 includes a body 1002. The sprocket 1000 includes consecutive first teeth 1004 and consecutive second teeth 1006 disposed on a perimeter 1008 of the body 1002. Each of the first teeth 1004 includes a first tooth body 1010 and a first load flank surface 1012. Each of the second teeth 1006 includes a second tooth body 1014 and an insert 1016 coupled to the second tooth body 1014. In the illustrated embodiment, each of the inserts 1016 form a corresponding second load flank surface 1018 of the second teeth 1006. The inserts 1016 of FIG. 20 do not cover respective clearance flank surfaces 1020 of the second teeth 1006. In other embodiments, the inserts 1016 cover the clearance flank surfaces 1020 of the second teeth 1006.In the illustrated embodiment, the first teeth 1004, including the first tooth bodies 1010 and the first load flank surfaces 1012, and the second tooth bodies 1014 are integrally formed and / or integrally formed. For example, the first teeth 1004, including the first tooth bodies 1010 and the first load flank surfaces 1012, and the second tooth bodies 1014 may be manufactured by stamping from a piece of a first material, such as an aluminum alloy. In other embodiments, the first teeth 1004, including the first tooth bodies 1010 and the first load flank surfaces 1012, and the second tooth bodies 1014 may be formed from one piece of a material different from an aluminum alloy and / or from two or more pieces. In some embodiments, the first load flank surfaces 1012 of the first teeth 1004 have a first wear resistance. In some embodiments, the first load flank surfaces 1012 of the first teeth 1004 have a first flatness, a first hardness, and / or one or more further and / or alternative features that enable the first load flank surfaces 1012 to have the first wear resistance.In the illustrated embodiment, the inserts 1016 are made of a second material different from the first material. For example, the inserts 1016 may be made of alloyed carbon steel, a titanium alloy, and / or one or more other and / or alternative materials. As a result, the second load flank surfaces 1018 formed by the inserts 1016 have a second wear resistance that is higher than the first wear resistance. In some embodiments, the second load flank surfaces 1018 of the second teeth 1006 have a second flatness, more planar than the first flatness, a second hardness, more severe than the first hardness, a wear protection layer, and / or one or more further and / or alternative features that enable the second teeth 1006 to have the second wear resistance.The first crank arm 906, the second crank arm 908, and the carrier 904 of FIG. 19 may be coupled to the sprocket 1000 to form a crank assembly. In such embodiments, the second teeth 1006 of the sprocket 1000 may be positioned relative to the crank arm 906 such that at least one of the second teeth 1006 is permitted to engage a chain 1022 and exert a maximum force on the chain 1022 during a maximum torque portion of a pedal revolution of the first crank arm 906. For example, the second teeth 1006 on the sprocket 1000 may be arranged in sequence between a first predetermined angle and a second predetermined angle behind the first longitudinal axis 912 of the first crank arm 906 relative to the direction of travel DD, as indicated by angle 1 and angle 2, respectively, in FIG. 19.The first teeth 1004 are at positions on the sprocket 1000 relative to the first crank arm 906 that allow at least one of the first teeth 1004 to engage the chain 1022 and exert a minimum force on the chain 1022 during the initial subsequent torque portion of the pedal revolution of the first crank arm 906. Further, the first teeth 1004 are at positions on the sprocket 1000 relative to the second crank arm 908 that allow at least one of the first teeth 1004 to engage the chain 1022 and exert a minimum force on the chain 1022 during the initial minimum torque portion of the pedal revolution of the second crank arm 908. For example, the first teeth 1004 on the sprocket 1000 may be arranged in sequence between a third predetermined angle forward of the first longitudinal axis 912 of the first crank arm 906 relative to the travel direction DD and a fourth predetermined angle rearward of the first longitudinal axis 912 of the first crank arm 906 relative to the travel direction DD, as indicated by the angle 7 and the angle 8, respectively, in FIG. 19.FIG. 22 is a perspective view of another example sprocket 1100 disclosed herein. In the illustrated embodiment, the sprocket 1100 includes a body 1102 having a periphery 1104. The teeth 1106 are arranged in succession on the circumference 1104. Each of the teeth 1106 of FIG. 22 includes a tooth body 1108 and an insert 1110 coupled to the tooth body 1108. Each of the inserts 1110 forms a load flank surface 1112 for each of the teeth 1106.In the illustrated embodiment, the tooth bodies 1108 and the body 1102 of the sprocket 1100 are integrally formed and / or integrally formed. For example, the tooth bodies 1108 and the body 1102 of the sprocket 1100 may be integrally stamped from a first material, such as an aluminum alloy. In other embodiments, the tooth bodies 1108 and the body 1102 may be formed from one piece of a material different from an aluminum alloy and / or from two or more pieces.In the illustrated embodiment, the inserts 1110 are made of a second material different from the first material. For example, the inserts 1110 may be of alloyed carbon steel, titanium alloy, and / or one or more other and / or alternative materials. As a result, the load flank surfaces 1112 formed by the inserts 1110 have a wear resistance that is higher than if the load flank surfaces 1112 were formed from the first material. In some embodiments, the load flank surfaces 1112 have a predetermined flatness, hardness, anti-wear layer, and / or one or more other and / or alternative features that allow the teeth 1106 to have the wear resistance.In view of the foregoing description, numerous modifications of the embodiments disclosed herein will be apparent to those skilled in the art. For example, each of the embodiments disclosed herein may be modified to include any of the structures or / or methods disclosed in connection with other embodiments. Accordingly, this disclosure is to be considered as illustrative only; it is intended to enable those skilled in the art to make and use the invention and to teach the best mode thereof. The exclusive rights in all modifications that fall within the scope of the appended claims are reserved.

Claims

A crank assembly for a bicycle, comprising: a sprocket (302) having first teeth (708) and second teeth (714), the first teeth (708) each comprising a first load flank surface (710) having a first wear resistance, the second teeth (714) each comprising a second load flank surface (716) having a second wear resistance that is higher than the first wear resistance; and a crank arm (306) coupled to the sprocket (302), the second teeth (714) being sequentially disposed on the sprocket (302) between more than 60 degrees and less than 110 degrees with respect to a longitudinal axis of the crank arm (306) in a direction opposite the direction of travel.The crank assembly of claim 1, wherein the sprocket (302) comprises a body (310) having a first circumferential portion (732), the first teeth (708) integral therewith, and a second circumferential portion (734) that does not comprise teeth, in particular wherein the sprocket (302) comprises a carrier (712) comprising the second teeth (714), the carrier (712) being retained on the second circumferential portion (734) of the sprocket (302).The crank assembly of any preceding claim, wherein each of the second teeth (714) comprises a wear protection layer to enable the second teeth (714) to have the second wear resistance.The crank assembly of any preceding claim, further comprising an insert (1016) coupled to each of the second teeth (1006), each of the inserts (1016) forming a respective one of the second load flank surfaces (1018), and / or further comprising a carrier (904) coupled to the sprocket (1000), the carrier (904) coupled to the crank arm (906).The crank assembly of claim 4, wherein the sprocket (902) comprises a first portion (926) and a second portion (928) coupled to the first portion (926), wherein the first portion (926) comprises the first teeth (934), the second portion (928) comprises the second teeth (936), and wherein an arm (918) of the carrier (904) overlaps the second portion (928), preferably wherein a connecting member (950) extends through the carrier (904) and the second portion (928).The crank assembly of any preceding claim, further comprising a second crank arm (307) coupled to the sprocket (302), the sprocket (302) comprising third teeth (720) each having a third load flank surface (722) with the second wear resistance, the third teeth on the sprocket (302) being disposed between greater than 60 degrees and less than 110 degrees with respect to a longitudinal axis of the second crank arm (307) in a direction opposite the direction of travel.A crank assembly, comprising: a crank arm (306); and only one sprocket (302) coupled to the crank arm (306), the sprocket (302) comprising a first tooth (708) and a second tooth (714), the first tooth (708) comprising a first load flank surface (710) having a first wear resistance, the second tooth (714) comprising a second load flank surface (716) having a second wear resistance that is higher than the first wear resistance; the second tooth (714) being relative to the crank arm (306) at a position on the sprocket (302) that is to allow the second tooth (714) to apply a maximum force to a chain (304) during a portion of maximum torque of a pedal revolution of the crank arm (306).The crank assembly of claim 7, wherein the first tooth (708) is at a position on the sprocket (302) relative to the crank arm (306) to allow the first tooth (708) to exert a minimum force on the chain (304) during a portion of minimum torque of pedal rotation of the crank arm (306).The crank assembly of claim 7 or 8, further comprising a carrier (904) coupled to the sprocket (902), the carrier (904) comprising a first arm (916), a second arm (918), and a third arm (920), in particular wherein the sprocket (902) comprises a first bridge member (926) and a second bridge member (928) releasably coupled to the first bridge member (926), wherein the first bridge member (926) comprises the first tooth (934) and is retained by the first arm (916) and the second arm (918), and the second bridge member (928) comprises the second tooth (936) and is retained by the second arm (918) and the third arm (920).The crank assembly of any of claims 7 to 9, wherein the second tooth (1006) comprises an insert (1016) forming the second load flank surface (1018) of the second tooth (1006).A crank assembly comprising: a first portion (926) of a sprocket (902) comprising first teeth (934) of a first material; a second portion (928) of the sprocket (902) coupled to the first portion (926), the second portion (928) comprising second teeth (936) of a second material different from the first material; and a carrier (904) comprising an arm (918) that overlaps the second portion (928) of the sprocket (902), characterized in that a first connecting member (950) releasably couples the first portion (926) and the second portion (928) to the arm (918) of the carrier (904).The crank assembly of claim 11, wherein the arm (918) overlaps with the first portion (926) of the sprocket (902).The crank assembly of claim 12, further comprising a connecting member (950) extending through the first section (926), the second section (928), and the bracket (904).The crank assembly of any of claims 11 to 13, wherein the bracket (904) comprises a second arm (918), the first section (926) spans a first space (942) between the first arm (916) and the second arm (918), in particular wherein the bracket (904) further comprises a third arm (920), the second section (928) spans a space (944) between the second arm (918) and the third arm (920).The crank assembly of any of claims 11 to 14, further comprising: a first crank arm (906) coupled to the carrier (904), wherein the second teeth (936) of the second portion (928) are provided on the sprocket (902) to follow a longitudinal axis of the crank arm (906) in a direction of travel of the crank arm, a second crank arm (908) coupled to the carrier (904); and a third portion (930) of the sprocket (902) coupled to the first portion (926), wherein the third portion (930) comprises third teeth (938) of the second material, wherein the third teeth (938) follow a longitudinal axis of the second crank arm (908) in the direction of travel.A sprocket for a crank assembly according to any preceding claim, comprising: a first portion (700) comprising consecutive first teeth (708), each of the first teeth (708) having a first load flank surface (710) with a first wear resistance; and a second portion (702) coupled to the first portion (700), the second portion (702) comprising consecutive second teeth (714), each of the second teeth (714) having a second load flank surface (716) with a second wear resistance that is higher than the first wear resistance, the consecutive second teeth (714) extending over an arc length corresponding to between a twelfth and a third of a circumference of a pitch circle (344) of the sprocket (302).The sprocket of claim 16, further comprising a third section (704) comprising successive third teeth (720), each of the third teeth (720) having a third load flank surface (722) with a third wear resistance that is higher than the first wear resistance, the third section (704) diametrically opposite the second section (702).The sprocket of claim 17, wherein the third wear resistance is equal to the second wear resistance.The sprocket of claim 17 or 18, wherein the third teeth (720) extend an arc length corresponding to between one-twelfth and one-third of the circumference of the pitch circle (344) of the sprocket (302).The sprocket of any of claims 16 to 19, further comprising a fourth section (706) comprising consecutive fourth teeth (724), each of the fourth teeth (724) comprising a fourth load flank surface (726) having the first wear resistance, in particular wherein the fourth section (706) is diametrically opposed to the first section (700), wherein the sprocket (302) comprises only the first (700), second (702), third (704), and fourth sections (706).The sprocket of any of claims 16 to 20, wherein the first section (700) is releasably coupled to a first portion of the sprocket and the second section (702) is releasably coupled to a second portion of the sprocket.The sprocket for a crank assembly of any of claims 1 to 15, comprising: a first tooth (708) comprising a first load flank surface (710) having a first wear resistance; a second tooth (714) having a second load flank surface (716) having a second wear resistance that is higher than the first wear resistance; and a third tooth (720) disposed following the second tooth (714), the third tooth (720) having a third load flank surface (722) having the second wear resistance, the second tooth (714) having a different thickness than the third tooth (720).The sprocket of claim 22, further comprising a body (310) having a first circumferential portion (732) and a second circumferential portion (734), wherein the first circumferential portion (732) is integrally formed with the first tooth (708), the second circumferential portion (734) does not comprise teeth, in particular wherein the sprocket (302) further comprises a carrier (712) comprising the second tooth (714), wherein the carrier (712) is disposed on the second circumferential portion (734) of the body (310).The sprocket of claim 22 or 23, wherein the second tooth (714) comprises a protrusion extending from a side of the second tooth (714), and / or wherein the first tooth (708) has substantially the same thickness as the second tooth (714).The sprocket of claim 22, wherein a first tooth tip of the first tooth (708) has a different thickness than a second tooth tip of the second tooth (714).The sprocket (902) for a crank assembly (900) of claim 11, wherein the sprocket (902) comprises: a first portion (926) comprising first teeth (934) of a first material; a second portion (928) coupled to the first portion (926), the second portion (928) comprising second teeth (936) of a second material different from the first material, the sprocket (902) configured to couple to a carrier (904) of the crank assembly (900), the carrier (904) comprising an arm (918) overlapping with the second portion (928) of the sprocket (902).

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