Patent Publication Number: US-10309266-B2

Title: Variable travel valve apparatus for an internal combustion engine

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 14/021,548, (now U.S. Pat. No. 9,145,797), entitled “Variable Travel Valve Apparatus for an Internal Combustion Engine,” filed on Sep. 9, 2013, which is a continuation of U.S. patent application Ser. No. 12/394,700 (now U.S. Pat. No. 8,528,511), entitled “Variable Travel Valve Apparatus for an Internal Combustion Engine,” filed on Feb. 27, 2009, which is a continuation-in-part of U.S. Pat. No. 7,874,271 entitled “Valve Apparatus for an Internal Combustion Engine,” and filed Dec. 8, 2008, which is a continuation of U.S. Pat. No. 7,461,619 entitled “Valve Apparatus for an Internal Combustion Engine,” and filed Sep. 22, 2006, which claims priority to U.S. Provisional Application Ser. No. 60/719,506 entitled “Side Cam Open Port,” filed Sep. 23, 2005 and U.S. Provisional Application Ser. No. 60/780,364 entitled “Side Cam Open Port Engine with Improved Head Valve,” filed Mar. 9, 2006; each of which is incorporated herein by reference in its entirety. 
     This application is related to U.S. patent application Ser. No. 11/534,508 (now U.S. Pat. No. 8,108,995), entitled “Valve Apparatus for an Internal Combustion Engine,” filed on Sep. 22, 2006, which is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     The embodiments described herein relate to an apparatus for controlling gas exchange processes in a fluid processing machine, and more particularly to a valve and cylinder head assembly for an internal combustion engine. 
     Many fluid processing machines, such as, for example, internal combustion engines, compressors, and the like, require accurate and efficient gas exchange processes to ensure optimal performance. For example, during the intake stroke of an internal combustion engine, a predetermined amount of air and fuel must be supplied to the combustion chamber at a predetermined time in the operating cycle of the engine. The combustion chamber then must be sealed during the combustion event to prevent inefficient operation and/or damage to various components in the engine. During the exhaust stroke, the burned gases in the combustion chamber must be efficiently evacuated from the combustion chamber. 
     Some known internal combustion engines use poppet valves to control the flow of gas into and out of the combustion chamber. Known poppet valves are reciprocating valves that include an elongated stem and a broadened sealing head. In use, known poppet valves open inwardly towards the combustion chamber such that the sealing head is spaced apart from a valve seat, thereby creating a flow path into or out of the combustion chamber when the valve is in the opened position. The sealing head can include an angled surface configured to contact a corresponding surface on the valve seat when the valve is in the closed position to effectively seal the combustion chamber. 
     The enlarged sealing head of known poppet valves, however, obstructs the flow path of the gas coming into or leaving the combustion cylinder, which can result in inefficiencies in the gas exchange process. Moreover, the enlarged sealing head can also produce vortices and other undesirable turbulence within the incoming air, which can negatively impact the combustion event. To minimize such effects, some known poppet valves are configured to travel a relatively large distance between the closed position and the opened position. Increasing the valve lift, however, results in higher parasitic losses, greater wear on the valve train, greater chance of valve-to-piston contact during engine operation, and the like. 
     Because the sealing head of known poppet valves extends into the combustion chamber, they are exposed to the extreme pressures and temperatures of engine combustion, which increases the likelihood that the valves will fail or leak. Exposure to combustion conditions can cause, for example, greater thermal expansion, detrimental carbon deposit build-up and the like. Moreover, such an arrangement is not conducive to servicing and/or replacing valves. In many instances, for example, the cylinder head must be removed to service or replace the valves. 
     To reduce the likelihood of leakage, known poppet valves are biased in the closed position using relatively stiff springs. Thus, known poppet valves are often actuated using a camshaft to produce the high forces necessary to open the valve. Known camshaft-based actuation systems, however, have limited flexibility to change the valve travel (or lift), timing and/or duration of the valve event as a function of engine operating conditions. For example, although some known camshaft-based actuation systems can change the valve opening or duration, such changes are limited because the valve events are dependent on the rotational position of the camshaft and/or the engine crankshaft. Accordingly, the valve events (i.e., the timing, duration and/or travel) are not optimized for each engine operating condition (e.g., low idle, high speed, full load, etc.), but are rather selected as a compromise that provides the desired overall performance. 
     Some known poppet valves are actuated using electronic actuators. Such solenoid-based actuation systems, however, often require multiple springs and/or solenoids to overcome the force of the biasing spring. Moreover, solenoid-based actuation systems require relatively high power to actuate the valves against the force of the biasing spring. 
     Thus, a need exists for an improved valve actuation system for an internal combustion engine and like systems and devices. 
     SUMMARY 
     Gas exchange valves and methods are described herein. In some embodiments, an apparatus includes a valve and an actuator. The valve has a portion movably disposed within a valve pocket defined by a cylinder head of an engine. The valve is configured to move relative to the cylinder head a distance between a closed position and an opened position. The portion of the valve defines a flow opening that is in fluid communication with a cylinder of an engine when the valve is in the opened position. The actuator is configured to selectively vary the distance between the closed position and the opened position. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1 and 2  are schematics illustrating a cylinder head assembly according to an embodiment in a first configuration and a second configuration, respectively. 
         FIGS. 3 and 4  are schematics illustrating a cylinder head assembly according to an embodiment in a first configuration and a second configuration, respectively. 
         FIG. 5  is a cross-sectional front view of a portion of an engine including a cylinder head assembly according to an embodiment in a first configuration. 
         FIG. 6  is a cross-sectional front view of the cylinder head assembly illustrated in  FIG. 5  in a second configuration 
         FIG. 7  is a cross-sectional front view of the portion of the cylinder head assembly labeled “ 7 ” in  FIG. 5 . 
         FIG. 8  is a cross-sectional front view of the portion of the cylinder head assembly labeled “ 8 ” in  FIG. 6 . 
         FIG. 9  is a top view of a portion of cylinder head assembly according to an embodiment. 
         FIGS. 10 and 11  are top and front views, respectively, of the valve member illustrated in  FIG. 5 . 
         FIG. 12  is a cross-sectional view of the valve member illustrated in  FIG. 11  taken along line  12 - 12 . 
         FIG. 13  is a perspective view of the valve member illustrated in  FIGS. 10-12 . 
         FIG. 14  is a perspective view of a valve member according to an embodiment. 
         FIGS. 15 and 16  are top and front views, respectively, of a valve member according to an embodiment. 
         FIG. 17  is a perspective view of a valve member according to an embodiment. 
         FIG. 18  is a perspective view of a valve member according to an embodiment. 
         FIG. 19  is a perspective view of a valve member according to an embodiment. 
         FIGS. 20 and 21  are front cross-sectional and side cross-sectional views, respectively, of a cylinder head assembly according to an embodiment. 
         FIG. 22  is a front cross-sectional view of a portion of a cylinder head assembly according to an embodiment. 
         FIG. 23  is a front cross-sectional view of a cylinder head assembly according to an embodiment. 
         FIGS. 24 and 25  are front cross-sectional and side cross-sectional views, respectively, of a cylinder head assembly according to an embodiment. 
         FIG. 26  is a cross-sectional view of a valve member according to an embodiment. 
         FIG. 27  is a perspective view of a valve member according to an embodiment having a one-dimensional tapered portion. 
         FIG. 28  is a front view of a valve member according to an embodiment. 
         FIGS. 29 and 30  are front cross-sectional views of a portion of a cylinder head assembly according to an embodiment in a first configuration and a second configuration, respectively. 
         FIG. 31  is a top view of a portion of an engine according to an embodiment. 
         FIG. 32  is a schematic illustrating a portion of an engine according to an embodiment. 
         FIG. 33  is a schematic illustrating a portion of the engine shown in  FIG. 32  operating in a pumping assist mode. 
         FIGS. 34-36  are graphical representations of the valve events of an engine according to an embodiment operating in a first mode and second mode, respectively. 
         FIG. 37  is a perspective exploded view of the cylinder head assembly shown in  FIG. 5 . 
         FIG. 38  is a flow chart illustrating a method of assembling an engine according to an embodiment. 
         FIG. 39  is a flow chart illustrating a method of repairing an engine according to an embodiment. 
         FIGS. 40 and 42  are schematic illustrations of top view of an engine having a variable travel valve actuator assembly in a closed position and in a first configuration and a second configuration, respectively, according to an embodiment. 
         FIGS. 41 and 43  are schematic illustrations of top view of the engine shown in  FIGS. 40 and 42  in an opened position and in a first configuration and a second configuration, respectively. 
         FIGS. 44 and 45  are schematic illustrations of top view of an engine having a variable travel valve actuator assembly in a closed position and in a first configuration and a second configuration, respectively, according to an embodiment. 
         FIGS. 46 and 47  are perspective views of an engine according to an embodiment. 
         FIG. 48  is a side view of a cylinder head, an intake valve actuator assembly, and an exhaust valve actuator assembly of the engine shown in  FIGS. 46 and 47 . 
         FIG. 49  is a top perspective exploded view of a portion of the engine shown in  FIGS. 46 and 47 . 
         FIG. 50  is a perspective exploded view of the intake valve actuator assembly of the engine shown in  FIGS. 46 and 47 . 
         FIGS. 51 and 52  are side cross-sectional views of a portion of the engine shown in  FIGS. 46 and 47 , with the intake valve in a closed position and a first opened position, respectively. 
         FIG. 53  is a side cross-sectional views of a portion of the engine shown in  FIGS. 46 and 47 , with the intake valve in a second opened position. 
         FIG. 54  is a top perspective view of the intake valve of the engine shown in  FIG. 49 . 
         FIG. 55  is a side cross-sectional view of the intake valve shown in  FIG. 54  taken along line X 1 -X 1  in  FIG. 54 . 
         FIG. 56  is a front view of the intake valve shown in  FIG. 54 . 
         FIG. 57  is a cross-sectional view of a portion of the intake valve actuator assembly. 
         FIG. 58  is a perspective exploded view of the exhaust valve actuator assembly of the engine shown in  FIGS. 46 and 47 . 
         FIGS. 59 and 60  are side cross-sectional views of a portion of the engine shown in  FIGS. 46 and 47 , with the exhaust valve in a closed position and a first opened position, respectively. 
         FIG. 61  is a side cross-sectional views of a portion of the engine shown in  FIGS. 46 and 47 , with the exhaust valve in a second opened position. 
         FIG. 62  is a top perspective view of the exhaust valve of the engine shown in  FIG. 49 . 
         FIG. 63  is a side cross-sectional view of the exhaust valve shown in  FIG. 62  taken along line X 2 -X 2  in  FIG. 62 . 
         FIG. 64  is a front view of the intake valve shown in  FIG. 62 . 
         FIG. 65  is a schematic illustration of an engine having an engine control unit (ECU) according to an embodiment. 
         FIGS. 66-68  are graphical representation of calibration tables contained within the ECU shown in  FIG. 65 . 
     
    
    
     DETAILED DESCRIPTION 
     In some embodiments, an apparatus includes a valve and an actuator. The valve has a portion movably disposed within a valve pocket defined by a cylinder head of an engine. The valve is configured to move relative to the cylinder head a distance between a closed position and an opened position. The portion of the valve defines a flow opening that is in fluid communication with a cylinder of an engine when the valve is in the opened position. The actuator is configured to selectively vary the distance between the closed position and the opened position. 
     In some embodiments, an apparatus includes a valve and an actuator. The valve has a portion movably disposed within a flow passageway defined by a cylinder head of an engine. The valve is configured to move relative to the cylinder head a distance between a closed position and an opened position. The valve is configured to move independent of the rotation of a crankshaft of the engine. The valve is disposed outside of a cylinder of the engine when the valve is in the opened position. The actuator is configured to selectively vary the distance between the closed position and the opened position. 
     In some embodiments, an apparatus includes a valve, a biasing member and an actuator. The valve has a portion movably disposed within a flow passageway defined by a cylinder head of an engine. The valve is configured to move relative to the cylinder head a distance between a closed position and an opened position. The valve is configured to move independent of the rotation of a crankshaft of the engine. The biasing member, which can be, for example, a spring, is configured to bias the valve towards the closed position. The biasing member is configured to exert a force on the valve when the valve is in the closed position. The actuator is configured to selectively vary the distance between the closed position and the opened position. The force exerted by the biasing member on the valve is maintained at a substantially constant value when the valve is in the closed position. Similarly stated, the actuator is configured to selectively vary the valve travel without changing the force exerted by the biasing member on the valve when the valve is in the closed position. 
       FIGS. 1 and 2  are schematic illustrations of a cylinder head assembly  130  according to an embodiment in a first and second configuration, respectively. The cylinder head assembly  130  includes a cylinder head  132  and a valve member  160 . The cylinder head  132  has an interior surface  134  that defines a valve pocket  138  having a longitudinal axis Lp. The valve member  160  has tapered portion  162  defining two flow passages  168  and having a longitudinal axis Lv. The tapered portion  162  includes two sealing portions  172 , each of which is disposed adjacent one of the flow passages  168 . The tapered portion  162  includes a first side surface  164  and a second side surface  165 . The second side surface  165  of the tapered portion  162  is angularly offset from the longitudinal axis Lv by a taper angle Θ, thereby producing the taper of the tapered portion  162 . Although the first side surface  164  is shown as being substantially parallel to the longitudinal axis Lv, thereby resulting in an asymmetrical tapered portion  162 , in some embodiments, the first side surface  164  is angularly offset such that the tapered portion  162  is symmetrical about the longitudinal axis Lv. Although the tapered portion  162  is shown as including a linear taper defining the taper angle Θ, in some embodiments the tapered portion  162  can include a non-linear taper. 
     The valve member  160  is reciprocatably disposed within the valve pocket  138  such that the tapered portion  162  of the valve member  160  can be moved along the longitudinal axis Lv of the tapered portion  162  within the valve pocket  138 . In use, the cylinder head assembly  130  can be placed in a first configuration ( FIG. 1 ) and a second configuration ( FIG. 2 ). As illustrated in  FIG. 1 , when in the first configuration, the valve member  160  is in a first position in which the sealing portions  172  are disposed apart from the interior surface  134  of the cylinder head  132  such that each flow passage  168  is in fluid communication with an area  137  outside of the cylinder head  132 . As illustrated in  FIG. 2 , the cylinder head assembly  132  is placed into the second configuration by moving the valve member  160  inwardly along the longitudinal axis Lv in the direction indicated by the arrow labeled A. When in the second configuration, the sealing portions  172  are in contact with a portion of the interior surface  134  of the cylinder head  132  such that each flow passage  168  is fluidically isolated from the area  137  outside of the cylinder head  132 . 
     Although the entire valve member  160  is shown as being tapered, in some embodiments, only a portion of the valve member is tapered. For example, as will be discussed herein, in some embodiments, a valve member can include one or more non-tapered portions. In other embodiments, a valve member can include multiple tapered portions. 
     Although the flow passages  168  are shown as being substantially normal to the longitudinal axis Lv of the valve member  160 , in some embodiments, the flow passages  168  can be angularly offset from the longitudinal axis Lv. Moreover, in some embodiments, the longitudinal axis Lv of the valve member  160  need not be coincident with the longitudinal axis Lp of the valve pocket  138 . For example, in some embodiments, the longitudinal axis of the valve member can be offset from and parallel to the longitudinal axis of the valve pocket. In other embodiments, the longitudinal axis of the valve can be disposed at an angle to the longitudinal axis of the valve pocket. 
     As illustrated, the longitudinal axis Lv of the tapered portion  162  is coincident with the longitudinal axis of the valve member. Accordingly, throughout the specification, the longitudinal axis of the tapered portion may be referred to as the longitudinal axis of the valve member and vice versa. In some embodiments, however, the longitudinal axis of the tapered portion can be offset from the longitudinal axis of the valve member. For example, in some embodiments, the first stem portion and/or the second stem portion as described below can be angularly offset from the tapered portion such that the longitudinal axis of the valve member is offset from the longitudinal axis of the tapered portion. 
     Although the cylinder head assembly  130  is illustrated as having a first configuration (i.e., an opened configuration) in which the flow passages  168  are in fluid communication with an area  137  outside of the cylinder head  132  and second configuration (i.e., a closed configuration) in which the flow passages  168  are fluidically isolated from the area  137  outside of the cylinder head  132 , in some embodiments the first configuration can be the closed configuration and the second configuration can be the opened configuration. In other embodiments, the cylinder head assembly  130  can have more than two configurations. For example, in some embodiments, a cylinder head assembly can have multiple open configurations, such as, for example, a partially opened configuration and a fully opened configuration. 
       FIGS. 3 and 4  are schematic illustrations of a portion of an engine  200  according to an embodiment in a first and second configuration, respectively. The engine  200  includes a cylinder head assembly  230 , a cylinder  203  and a gas manifold  210 . The cylinder  203  is coupled to a first surface  235  of the cylinder head assembly  230  and can be, for example, a combustion cylinder defined by an engine block (not shown). The gas manifold  210  is coupled to a second surface  236  of the cylinder head assembly  230  and can be, for example an intake manifold or an exhaust manifold. Although the first surface  235  and the second surface  236  are shown as being parallel to and disposed on opposite sides of the cylinder head  232  from each other, in other embodiments, the first surface and the second surface can be adjacent each other. In yet other embodiments, the gas manifold and the cylinder can be coupled to the same surface of the cylinder head. 
     The cylinder head assembly  230  includes a cylinder head  232  and a valve member  260 . The cylinder head  232  has an interior surface  234  that defines a valve pocket  238  having a longitudinal axis Lp. The cylinder head  232  also defines two cylinder flow passages  248  and two gas manifold flow passages  244 . Each of the cylinder flow passages  248  is in fluid communication with the cylinder  203  and the valve pocket  238 . Similarly, each of the gas manifold flow passages  244  is in fluid communication with the gas manifold  210  and the valve pocket  238 . Although each of the cylinder flow passages  248  is shown as being fluidically isolated from the other cylinder flow passage  248 , in other embodiments, the cylinder flow passages  248  can be in fluid communication with each other. Similarly, although each of the gas manifold flow passages  244  is shown as being fluidically isolated from the other gas manifold flow passage  244 , in other embodiments, the gas manifold flow passages  244  can be in fluid communication with each other. 
     The valve member  260  has a tapered portion  262  having a longitudinal axis Lv and a taper angle Θ with respect to the longitudinal axis Lv. The tapered portion  262  defines two flow passages  268  and includes two sealing portions  272 , each of which is disposed adjacent one of the flow passages  268 . Although shown as being an asymmetrical taper in a single dimension, in some embodiments the tapered portion can be symmetrically tapered about the longitudinal axis Lv. In other embodiments, as discussed in more detail herein, the tapered portion can be tapered in two dimensions about the longitudinal axis Lv. 
     The valve member  260  is disposed within the valve pocket  238  such that the tapered portion  262  of the valve member  260  can be moved along its longitudinal axis Lv within the valve pocket  238 . In use, the engine  200  can be placed in a first configuration ( FIG. 3 ) and a second configuration ( FIG. 4 ). As illustrated in  FIG. 3 , when in the first configuration, the valve member  260  is in a first position in which each flow passage  268  is in fluid communication with one of the cylinder flow passages  248  and one of the gas manifold flow passages  244 . In this manner, the gas manifold  210  is in fluid communication with the cylinder  203 . Although the flow passages  268  are shown as being aligned with the cylinder flow passages  248  and the gas manifold flow passages  244  when the engine is in the first configuration, in other embodiments the flow passages  268  need not be directly aligned. In other words, the flow passages  268 ,  248 ,  24  may be offset when the engine  200  is in the first configuration, but the gas manifold  210  is still in fluid communication with the cylinder  203 . 
     As illustrated in  FIG. 4 , when the engine  200  is in the second configuration, the valve member  260  is in a second position, axially offset from the first position in the direction indicated by the arrow labeled B. In the second configuration, the sealing portions  272  are in contact with a portion of the interior surface  234  of the cylinder head  232  such that each flow passage  268  is fluidically isolated from the cylinder flow passages  248 . In this manner, the cylinder  203  is fluidically isolated from the gas manifold  210 . 
       FIG. 5  is a cross-sectional front view of a portion of an engine  300  including a cylinder head assembly  330  in a first configuration according to an embodiment.  FIG. 6  is a cross-sectional front view of the cylinder head assembly  330  in a second configuration. The engine  300  includes an engine block  302  and a cylinder head assembly  330  coupled to the engine block  302 . The engine block  302  defines a cylinder  303  having a longitudinal axis Lc. A piston  304  is disposed within the cylinder  303  such that it can reciprocate along the longitudinal axis Lc of the cylinder  303 . The piston  304  is coupled by a connecting rod  306  to a crankshaft  308  having an offset throw  307  such that as the piston reciprocates within the cylinder  303 , the crankshaft  308  is rotated about its longitudinal axis (not shown). In this manner, the reciprocating motion of the piston  304  can be converted into a rotational motion. 
     A first surface  335  of the cylinder head assembly  330  is coupled to the engine block  302  such that a portion of the first surface  335  covers the upper portion of the cylinder  303  thereby forming a combustion chamber  309 . Although the portion of the first surface  335  covering the cylinder  303  is shown as being curved and angularly offset from the top surface of the piston, in some embodiments, because the cylinder head assembly  330  does not include valves that protrude into the combustion chamber, the surface of the cylinder head assembly forming part of the combustion chamber can have any suitable geometric design. For example, in some embodiments, the surface of the cylinder head assembly forming part of the combustion chamber can be flat and parallel to the top surface of the piston. In other embodiments, the surface of the cylinder head assembly forming part of the combustion chamber can be curved to form a hemispherical combustion chamber, a pent-roof combustion chamber or the like. 
     A gas manifold  310  defining an interior area  312  is coupled to a second surface  336  of the cylinder head assembly  330  such that the interior area  312  of the gas manifold  310  is in fluid communication with a portion of the second surface  336 . As described in detail herein, this arrangement allows a gas, such as, for example air or combustion by-products, to be transported into or out of the cylinder  303  via the cylinder head assembly  330  and the gas manifold  310 . Although shown as including a single gas manifold  310 , in some embodiments, an engine can include two or more gas manifolds. For example, in some embodiments an engine can include an intake manifold configured to supply air and/or an air-fuel mixture to the cylinder head and an exhaust manifold configured to transport exhaust gases away from the cylinder head. 
     Moreover, as shown, in some embodiments the first surface  335  can be opposite the second surface  336 , such that the flow of gas into and/or out of the cylinder  303  can occur along a substantially straight line. In such an arrangement, a fuel injector (not shown) can be disposed in an intake manifold (not shown) directly above the cylinder flow passages  348 . In this manner, the injected fuel can be conveyed into the cylinder  303  without being subjected to a series of bends. Eliminating bends along the fuel path can reduce fuel impingement and/or wall wetting, thereby leading to more efficient engine performance, such as, for example, improved transient response. 
     The cylinder head assembly  330  includes a cylinder head  332  and a valve member  360 . The cylinder head  332  has an interior surface  334  that defines a valve pocket  338  having a longitudinal axis Lp. The cylinder head  332  also defines four cylinder flow passages  348  and four gas manifold flow passages  344 . Each of the cylinder flow passages  348  is adjacent the first surface  335  of the cylinder head  332  and is in fluid communication with the cylinder  303  and the valve pocket  338 . Similarly, each of the gas manifold flow passages  344  is adjacent the second surface  336  of the cylinder head  332  and is in fluid communication with the gas manifold  310  and the valve pocket  338 . Each of the cylinder flow passages  348  is aligned with a corresponding gas manifold flow passage  344 . In this arrangement, when the cylinder head assembly  330  is in the first (or opened) configuration (see, e.g.,  FIGS. 5 and 7 ), the gas manifold  310  is in fluid communication with the cylinder  303 . Conversely, when the cylinder head assembly  330  is in a second (or closed) configuration (see, e.g.,  FIGS. 6 and 8 ), the gas manifold  310  is fluidically isolated from the cylinder  303 . 
     The valve member  360  has tapered portion  362 , a first stem portion  376  and a second stem portion  377 . The first stem portion  376  is coupled to an end of the tapered portion  362  of the valve member  360  and is configured to engage a valve lobe  315  of a camshaft  314 . The second stem portion  377  is coupled to an end of the tapered portion  362  opposite from the first stem portion  376  and is configured to engage a spring  318 . A portion of the spring  318  is contained within an end plate  323 , which is removably coupled to the cylinder head  332  such that it compresses the spring  318  against the second stem portion  377  thereby biasing the valve member  360  in a direction indicated by the arrow D in  FIG. 6 . 
     The tapered portion  362  of the valve member  360  defines four flow passages  368  therethrough. The tapered portion includes eight sealing portions  372  (see, e.g.,  FIGS. 10, 11 and 13 ), each of which is disposed adjacent one of the flow passages  368  and extends continuously around the perimeter of an outer surface  363  of the tapered portion  362 . The valve member  360  is disposed within the valve pocket  338  such that the tapered portion  362  of the valve member  360  can be moved along a longitudinal axis Lv of the valve member  360  within the valve pocket  338 . In some embodiments, the valve pocket  338  includes a surface  352  configured to engage a corresponding surface  380  on the valve member  360  to limit the range of motion of the valve member  360  within the valve pocket  338 . 
     In use, when the camshaft  314  is rotated such that the eccentric portion of the valve lobe  315  is in contact with the first stem  376  of the valve member  360 , the force exerted by the valve lobe  315  on the valve member  360  is sufficient to overcome the force exerted by the spring  318  on the valve member  360 . Accordingly, as shown in  FIG. 5 , the valve member  360  is moved along its longitudinal axis Lv within the valve pocket  338  in the direction of the arrow C, into a first position, thereby placing the cylinder head assembly  330  in the opened configuration. When in the opened configuration, the valve member  360  is positioned within the valve pocket  338  such that each flow passage  368  is aligned with and in fluid communication with one of the cylinder flow passages  348  and one of the gas manifold flow passages  344 . In this manner, the gas manifold  310  is in fluid communication with the cylinder  303 , along the flow path indicated by the arrow labeled E in  FIG. 7 . 
     When the camshaft  314  is rotated such that the eccentric portion of the camshaft lobe  315  is not in contact with the first stem  376  of the valve member  360 , the force exerted by the spring  318  is sufficient to move the valve member  360  in the direction of the arrow D, into a second position, axially offset from the first position, thereby placing the cylinder head assembly  330  in the closed configuration (see  FIG. 6 ). When in the closed configuration, each flow passage  368  is offset from the corresponding cylinder flow passage  348  and gas manifold flow passage  344 . Moreover, as shown in  FIG. 8 , when in the closed configuration, each of the sealing portions  372  is in contact with a portion of the interior surface  334  of the cylinder head  332  such that each flow passage  368  is fluidically isolated from the cylinder flow passages  348 . In this manner, the cylinder  303  is fluidically isolated from the gas manifold  310 . 
     Although the cylinder head assembly  330  is described as being configured to fluidically isolate the flow passages  368  from the cylinder flow passages  348  when in the closed configuration, in some embodiments, the sealing portions  372  can be configured to contact a portion of the interior surface  334  of the cylinder head  332  such that each flow passage  368  is fluidically isolated from the cylinder head flow passages  348  and the gas manifold flow passages  344 . In other embodiments, the sealing portions  372  can be configured to contact a portion of the interior surface  334  of the cylinder head  332  such that each flow passage  368  is fluidically isolated only from the gas manifold flow passages  344 . 
     Although each of the cylinder flow passages  348  is shown being fluidically isolated from the other cylinder flow passage  348 , in some embodiments, the cylinder flow passages  348  can be in fluid communication with each other. Similarly, although each of the gas manifold flow passages  344  is shown being fluidically isolated from the other gas manifold flow passages  344 , in other embodiments, the gas manifold flow passages  344  can be in fluid communication with each other. 
     Although the longitudinal axis Lc of the cylinder  303  is shown as being substantially normal to the longitudinal axis Lp of the valve pocket  338  and the longitudinal axis Lv of the valve  360 , in some embodiments, the longitudinal axis of the cylinder can be offset from the longitudinal axis of the valve pocket and/or the longitudinal axis of the valve member by an angle other than 90 degrees. In yet other embodiments, the longitudinal axis of the cylinder can be substantially parallel to the longitudinal axis of the valve pocket and/or the longitudinal axis of the valve member. Similarly, as described above, the longitudinal axis Lv of the valve member  360  need not be coincident with or parallel to the longitudinal axis Lp of the valve pocket  338 . 
     In some embodiments, the camshaft  314  is disposed within a portion of the cylinder head  332 . An end plate  322  is removably coupled to the cylinder head  332  to allow access to the camshaft  314  and the first stem portion  376  for assembly, repair and/or adjustment. In other embodiments, the camshaft is disposed within a separate cam box (not shown) that is removably coupled to the cylinder head. Similarly, the end plate  323  is removably coupled to the cylinder head  332  to allow access to the spring  318  and/or the valve member  360  for assembly, repair, replacement and/or adjustment. 
     In some embodiments, the spring  318  is a coil spring configured to exert a force on the valve member  360  thereby ensuring that the sealing portions  372  remain in contact with the interior surface  334  when the cylinder head assembly  330  is in the closed configuration. The spring  318  can be constructed from any suitable material, such as, for example, a stainless steel spring wire, and can be fabricated to produce a suitable biasing force. In some embodiments, however, a cylinder head assembly can include any suitable biasing member to ensure that that the sealing portions  372  remain in contact with the interior surface  334  when the cylinder head assembly  330  is in the closed configuration. For example, in some embodiments, a cylinder head assembly can include a cantilever spring, a Belleville spring, a leaf spring and the like. In other embodiments, a cylinder head assembly can include an elastic member configured to exert a biasing force on the valve member. In yet other embodiments, a cylinder head assembly can include an actuator, such as a pneumatic actuator, a hydraulic actuator, an electronic actuator and/or the like, configured to exert a biasing force on the valve member. 
     Although the first stem portion  376  is shown and described as being in direct contact with the valve lobe  315  of the camshaft  314 , in some embodiments, an engine and/or cylinder head assembly can include a member configured to maintain a predetermined valve lash setting, such as for example, an adjustable tappet, disposed between the camshaft and the first stem portion. In other embodiments, an engine and/or cylinder head assembly can include a hydraulic lifter disposed between the camshaft and the first stem portion to ensure that the valve member is in constant contact with the camshaft. In yet other embodiments, an engine and/or a cylinder head assembly can include a follower member, such as for example, a roller follower disposed between the first stem portion. Similarly, in some embodiments, an engine can include one or more components disposed adjacent the spring. For example, in some embodiments, the second stem portion can include a spring retainer, such as for example, a pocket, a clip, or the like. In other embodiments, a valve rotator can be disposed adjacent the spring. 
     Although the cylinder head  332  is shown and described as being a separate component coupled to the engine block  302 , in some embodiments, the cylinder head  332  and the engine block  302  can be monolithically fabricated, thereby eliminating the need for a cylinder head gasket and cylinder head mounting bolts. In some embodiments, for example, the engine block and the cylinder head can be cast using a single mold and subsequently machined to include the cylinders, valve pockets and the like. Moreover, as described above, the valve members can be installed and/or serviced by removing the end plate. 
     Although the engine  300  is shown and described as including a single cylinder, in some embodiments, an engine can include any number of cylinders in any arrangement. For example, in some embodiments, an engine can include any number of cylinders in an in-line arrangement. In other embodiments, any number of cylinders can be arranged in a vee configuration, an opposed configuration or a radial configuration. 
     Similarly, the engine  300  can employ any suitable thermodynamic cycle. Such engine types can include, for example, Diesel engines, spark ignition engines, homogeneous charge compression ignition (HCCI) engines, two-stroke engines and/or four stroke engines. Moreover, the engine  300  can include any suitable type of fuel injection system, such as, for example, multi-port fuel injection, direct injection into the cylinder, carburetion, and the like. 
     Although the cylinder head assembly  330  is shown and described above as being devoid of mounting holes, a spark plug, and the like, in some embodiments, a cylinder head assembly includes mounting holes, spark plugs, cooling passages, oil drillings and the like. 
     Although the cylinder head assembly  330  is shown and described above with reference to a single valve  360  and a single gas manifold  310 , in some embodiments, a cylinder head assembly includes multiple valves and gas manifolds. For example,  FIG. 9  illustrates a top view of the cylinder head assembly  330  including an intake valve member  360 I and an exhaust valve member  360 E. As illustrated, the cylinder head  332  defines an intake valve pocket  338 I, within which the intake valve member  360 I is disposed, and an exhaust valve pocket  338 E, within which the exhaust valve member  360 E is disposed. Similar to the arrangement described above, the cylinder head  332  also defines four intake manifold flow passages  344 I, four exhaust manifold flow passages  344 E and the corresponding cylinder flow passages (not shown in  FIG. 9 ). Each of the intake manifold flow passages  344 I is adjacent the second surface  336  of the cylinder head  332  and is in fluid communication with an intake manifold (not shown) and the intake valve pocket  338 I. Similarly, each of the exhaust manifold flow passages  344 E is adjacent the second surface  336  of the cylinder head  332  and is in fluid communication with an exhaust manifold (not shown) and the exhaust valve pocket  338 E. 
     The operation of the intake valve member  360 I and the exhaust valve member  360 E is similar to that of the valve member  360  described above in that each has a first (or opened) position and a second (or closed) position. In  FIG. 9 , the intake valve member  360 I is shown in the opened position, in which each flow passage  368 I defined by the tapered portion  362 I of the intake valve member  360 I is aligned with its corresponding intake manifold flow passage  344 I and cylinder flow passage (not shown). In this manner, the intake manifold (not shown) is in fluid communication with the cylinder  303 , thereby allowing a charge of air to be conveyed from the intake manifold into the cylinder  303 . Conversely, the exhaust valve member  360 E is shown in the closed position in which each flow passage  368 E defined by the tapered portion  362 E of the exhaust valve member  360 E is offset from its corresponding exhaust manifold flow passage  344 E and cylinder flow passage (not shown). Moreover, each sealing portion (not shown in  FIG. 9 ) defined by the exhaust valve member  360 E is in contact with a portion of the interior surface of the exhaust valve pocket  338 E such that each flow passage  368 E is fluidically isolated from the cylinder flow passages (not shown). In this manner, the cylinder  303  is fluidically isolated from the exhaust manifold (not shown). 
     The cylinder head assembly  330  can have many different configurations corresponding to the various combinations of the positions of the valve members  360 I,  360 E as they move between their respective first and second positions. One possible configuration includes an intake configuration in which, as shown in  FIG. 9 , the intake valve member  360 I is in the opened position and the exhaust valve member  360 E is in the closed position. Another possible configuration includes a combustion configuration in which both valves are in their closed positions. Yet another possible configuration includes an exhaust configuration in which the intake valve member  360 I is in the closed position and the exhaust valve member  360 E is in the opened position. Yet another possible configuration is an overlap configuration in which both valves are in their opened positions. 
     Similar to the operation described above, the intake valve member  360 I and the exhaust valve member  360 E are moved by a camshaft  314  that includes an intake valve lobe  315 I and an exhaust valve lobe  315 E. As shown, the intake valve member  360 I and the exhaust valve member  360 E are each biased in the closed position by springs  318 I,  318 E, respectively. Although the intake valve lobe  315 I and the exhaust valve lobe  315 E are illustrated as being disposed on a single camshaft  314 , in some embodiments, an engine can include separate camshafts to move the intake and exhaust valve members. In other embodiments, as discussed herein, the intake valve member  360 I and/or the exhaust valve member  360 E can be moved by an suitable means, such as, for example, an electronic solenoid, a stepper motor, a hydraulic actuator, a pneumatic actuator, a piezo-electric actuator or the like. In yet other embodiments, the intake valve member  360 I and/or the exhaust valve member  360 E are not maintained in the closed position by a spring, but rather include mechanisms similar to those described above for moving the valve. For example, in some embodiments, a first stem of a valve member can engage a camshaft valve lobe and the second stem of the valve member can engage a solenoid configured to bias the valve member. 
       FIGS. 10-13  show a top view, a front view, a side cross-sectional view and a perspective view of the valve member  360 , respectively. As described above, the valve member has tapered portion  362 , a first stem portion  376  and a second stem portion  377 . The tapered portion  362  of the valve member  360  defines four flow passages  368 . Each flow passage  368  extends through the tapered portion  362  and includes a first opening  369  and a second opening  370 . In the illustrated embodiment, the flow passages  368  are spaced apart by a distance S along the longitudinal axis Lv of the tapered portion  362 . The distance S corresponds to the distance that the tapered portion  362  moves within the valve pocket  338  when transitioning from the first (opened configuration) to the second (closed) configuration. Accordingly, the travel (or stroke) of the valve member can be reduced by spacing the flow passages  368  closer together. In some embodiments, the distance S can be between 2.3 mm and 4.2 mm (0.090 in. and 0.166 in.). In other embodiments, the distance S can be less than 2.3 mm (0.090 in.) or greater than 4.2 mm (0.166 in.). Although illustrated as having a constant spacing S, in some embodiments, the flow passages are each separated by a different distance. As discussed in more detail herein, reducing the stroke of the valve member can result in several improvements in engine performance, such as, for example, reduced parasitic losses, allowing the use of weaker valve springs, and the like. 
     Although the tapered portion  362  is shown as defining four flow passages having a long, narrow shape, in some embodiments a valve member can define any number of flow passages having any suitable shape and size. For example, in some embodiments, a valve member can include eight flow passages configured to have approximately the same cumulative flow area (as taken along a plane normal to the longitudinal axis Lf of the flow passages) as that of a valve member having four larger flow passages. In such an embodiment, the flow passages can be arranged such that the spacing between the flow passages of the “eight passage valve member” is approximately half that of the of the spacing between the flow passages of the “four passage valve member.” As such, the stroke of the “eight passage valve member” is approximately half that of the “four passage valve member,” thereby resulting in an arrangement that provides substantially the same flow area while requiring the valve member to move only approximately half the distance. 
     Each flow passage  368  need not have the same shape and/or size as the other flow passages  368 . Rather, as shown, the size of the flow passages can decrease with the taper of the tapered portion  362  of the valve member  360 . In this manner, the valve member  360  can be configured to maximize the cumulative flow area, thereby resulting in more efficient engine operation. Moreover, in some embodiments, the shape and/or size of the flow passages  368  can vary along the longitudinal axis Lf. For example, in some embodiments, the flow passages can have a lead-in chamfer or taper along the longitudinal axis Lf. 
     Similarly, each of the manifold flow passages  344  and each of the cylinder flow passages  348  need not have the same shape and/or size as the other manifold flow passages  344  and each of the cylinder flow passages  348 , respectively. Moreover, in some embodiments, the shape and/or size of the manifold flow passages  344  and/or the cylinder flow passages  348  can vary along their respective longitudinal axes. For example, in some embodiments, the manifold flow passages can have a lead in chamfer or taper along their longitudinal axes. In other embodiments, the cylinder flow passages can have a lead-in chamfer or taper along their longitudinal axes. 
     Although the longitudinal axis Lf of the flow passages  368  is shown in  FIG. 12  as being substantially normal to the longitudinal axis Lv of the valve member  360 , in some embodiments the longitudinal axis Lf of the flow passages  368  can be angularly offset from the longitudinal axis Lv of the valve member  360  by an angle other than 90 degrees. Moreover, as discussed in more detail herein, in some embodiments, the longitudinal axis and/or the centerline of one flow passage need not be parallel to the longitudinal axis of another flow passage. 
     As previously discussed with reference to  FIG. 5 , the valve member  360  includes a surface  380  configured to engage a corresponding surface  352  within the valve pocket  338  to limit the range of motion of the valve member  360  within the valve pocket  338 . Although the surface  380  is illustrated as being a shoulder-like surface disposed adjacent the second stem portion  377 , in some embodiments, the surface  380  can have any suitable geometry and can be disposed anywhere along the valve member  360 . For example, in some embodiments, a valve member can have a surface disposed on the first stem portion, the surface being configured to limit the longitudinal motion of the valve member. In other embodiments, a valve member can have a flattened surface disposed on one of the stem portions, the flattened surface being configured to limit the rotational motion of the valve member. In yet other embodiments, as illustrated in  FIG. 37 , the valve member  360  can be aligned using an alignment key  398  configured to be disposed within a mating keyway  399 . 
     As shown in  FIG. 10 , which illustrates a top view of the valve member  360 , the first opposing side surfaces  364  of the tapered portion  362  are angularly offset from each other by a first taper angle Θ. Similarly, as shown in  FIG. 11 , which presents a front view of the valve member  360 , the second opposing side surfaces  365  of the tapered portion  362  are angularly offset from each other by an angle α. In this manner, the tapered portion  362  of the valve member  360  is tapered in two dimensions. 
     Said another way, the tapered portion  362  of the valve member  360  has a width W measured along a first axis Y that is normal to the longitudinal axis Lv. Similarly, the tapered portion  362  has a thickness T (not to be confused with the wall thickness of any portion of the valve member) measured along a second axis Z that is normal to both the longitudinal axis Lv and the first axis Y. The tapered portion  362  has a two-dimensional taper characterized by a linear change in the width W and a linear change in the thickness T. As shown in  FIG. 10 , the width of the tapered portion  362  increases from a value of W 1  at one end of the tapered portion  362  to a value of W 2  at the opposite end of the tapered portion  362 . The change in width along the longitudinal axis Lv defines the first taper angle Θ. Similarly, as illustrated in  FIG. 11 , the thickness of the tapered portion  362  increases from a value of T 1  at one end of the tapered portion  362  to a value of T 2  at the opposite end of the tapered portion  362 . The change in thickness along the longitudinal axis Lv defines the second taper angle α. 
     In the illustrated embodiment, the first taper angle Θ and the second taper angle α are each between 2 and 10 degrees. In some embodiments, the first taper angle Θ is the same as the second taper angle α. In other embodiments, the first taper angle Θ is different from the second taper angle α. Selection of the taper angles can affect the size of the valve member and the nature of the seal formed by the sealing portions  372  and the interior surface  334  of the cylinder head  332 . In some embodiments, for example, the taper angles Θ, α can be as high as 90 degrees. In other embodiments, the taper angles Θ, α can be as low as 1 degree. In yet other embodiments, as discussed in more detail herein, a valve member can be devoid of a tapered portion (i.e., a taper angle of zero degrees). 
     Although the tapered portion  362  is shown and described as having a single, linear taper, in some embodiments a valve member can include a tapered portion having a curved taper. In other embodiments, as discussed in more detail herein, a valve member can have a tapered portion having multiple tapers. Moreover, although the side surfaces  164 ,  165  are shown as being angularly offset substantially symmetrical to the longitudinal axis Lv, in some embodiments, the side surfaces can be angularly offset in an asymmetrical fashion. 
     As shown in  FIGS. 10, 11 and 13 , the tapered portion  362  includes eight sealing portions  372 , each extending continuously around the perimeter of the outer surface  363  of the tapered portion  362 . The sealing portions  372  are arranged such that two of the sealing portions  372  are disposed adjacent each flow passage  368 . In this manner, as shown in  FIG. 8 , when the cylinder head assembly  330  is in the closed position each of the sealing portions  372  is in contact with a portion of the interior surface  334  of the cylinder head  332  such that each flow passage  368  is fluidically isolated from the each cylinder flow passage  348  and/or each gas manifold flow passage  344 . Conversely, when the cylinder head assembly  330  is in the opened position each of the sealing portions  372  is disposed apart from the interior surface  334  of the cylinder head  332  such that each flow passage  368  is in fluid communication with the corresponding cylinder flow passages  348  and the corresponding gas manifold flow passages  344 . 
     Although the sealing portions  372  are shown and described as extending around the perimeter of the outer surface  363  substantially normal to the longitudinal axis Lv of the valve member  360 , in some embodiments, the sealing portions can be at any angular relation to the longitudinal axis Lv. Moreover, in some embodiments, the sealing portions  372  can be angularly offset from each other. 
     Although the sealing portions  372  are shown and described as being a locus of points continuously extending around the perimeter of the outer surface  363  of the tapered portion  362  in a linear fashion when viewed in a plane parallel to the longitudinal axis Lv and the first axis Y (i.e.,  FIG. 10 ), in some embodiments, the sealing portions can continuously extend around the outer surface in a non-linear fashion. For example, in some embodiments, the sealing portions, when viewed in a plane parallel to the longitudinal axis Lv and the first axis Y, can be curved. In other embodiments, for example, as shown in  FIG. 14 , the sealing portions can be two-dimensional.  FIG. 14  shows a valve member  460  having a tapered portion  472 , a first stem portion  476  and a second stem portion  477 . As described above, the tapered portion includes four flow passages  468  therethrough. The tapered portion also includes two sealing portions  472  disposed about each flow passage  468  and extending continuously around the perimeter of the outer surface  463  of the tapered portion  462  (for clarity, only two sealing portions  472  are shown). In contrast to the sealing portions  372  described above, the sealing portions  472  have a width X as measured along the longitudinal axis Lv of the valve member  460 . 
     As illustrated in  FIG. 12 , the tapered portion  362  has an elliptical cross-section, which can allow for both a sufficient taper and flow passages of sufficient size. In other embodiments, however, the tapered portion can have any suitable cross-sectional shape, such as, for example, a circular cross-section, a rectangular cross-section and the like. 
     As shown in  FIGS. 10-13 , the valve member  360  is monolithically formed to include the first stem portion  376 , the second stem portion  377  and the tapered portion  362 . In other embodiments, however, the valve member includes separate components coupled together to form the first stem portion, the second stem portion and the tapered portion. In yet other embodiments, the valve member does not include a first stem portion and/or a second stem portion. For example, in some embodiments, a cylinder head assembly includes a separate component disposed within the valve pocket and configured to engage a valve lobe of a camshaft and a portion of a valve member such that a force can be directly transmitted from the camshaft to the valve member. Similarly, in some embodiments, a cylinder head assembly includes a separate component disposed within the valve pocket and configured to engage a spring and a portion of a valve member such that a force can be transmitted from the spring to the valve member. 
     Although the sealing portions  372  and the outer surface  363  are shown and described as being monolithically constructed, in some embodiments, the sealing portions can be separate components coupled to the outer surface of the tapered portion. For example, in some embodiments, the sealing portions can be sealing rings that are held into mating grooves on the outer surface of the tapered portion by a friction fit. In other embodiments, the sealing portions are separate components that are bonded to the outer surface of the tapered portion by any suitable means, such as, for example, chemical bonding, thermal bonding and the like. In yet other embodiments, the sealing portions include a coating applied to the outer surface of the tapered portion by any suitable manner, such as for example, electrostatic spray deposition, chemical vapor deposition, physical vapor deposition, ionic exchange coating, and the like. 
     The valve member  360  can be fabricated from any suitable material or combination of materials. For example, in some embodiments, the tapered portion can be fabricated from a first material, the stem portions can be fabricated from a second material different from the first material and the sealing portions, to the extent that they are separately formed, can be fabricated from a third material different from the first two materials. In this manner, each portion of the valve member can be constructed from a material that is best suited for its intended function. For example, in some embodiments, the sealing portions can be fabricated from a relatively soft stainless steel, such as for example, unhardened 430FR stainless steel, so that the sealing portions will readily wear when contacting the interior surface of the cylinder head. In this manner, the valve member can be continuously lapped during use, thereby ensuring a fluid-tight seal. In some embodiments, for example, the tapered portion can be fabricated from a relatively hard material having high strength, such as for example, hardened 440 stainless steel. Such a material can provide the necessary strength and/or hardness to resist failure that may result from repeated exposure to high temperature exhaust gas. In some embodiments, for example, one or both stem portions can be fabricated from a ceramic material configured to have high compressive strength. 
     In some embodiments, the cylinder head  332 , including the interior surface  334  that defines the valve pocket  338 , is monolithically constructed from a single material, such as, for example, cast iron. In some monolithic embodiments, for example, the interior surface  334  defining the valve pocket  338  can be machined to provide a suitable surface for engaging the sealing portions  372  of the valve member  360  such that a fluid-tight seal can be formed. In other embodiments, however, the cylinder head can be fabricated from any suitable combination of materials. As discussed in more detail herein, in some embodiments, a cylinder head can include one or more valve inserts disposed within the valve pocket. In this manner, the portion of the interior surface configured to contact the sealing portions of the valve member can be constructed from a material and/or in a manner conducive to providing a fluid-tight seal. 
     Although the flow passages  368  are shown and described as extending through the tapered portion  362  of the valve member  360  and having a first opening  369  and a second opening  370 , in other embodiments, the flow passages do not extend through the valve member.  FIGS. 15 and 16  show a top view and a front view, respectively, of a valve member  560  according to an embodiment in which the flow passages  568  extend around an outer surface  563  of the valve member  560 . Similar to the valve member  360  described above, the valve member  560  includes a first stem portion  576 , a second stem portion  577  and a tapered portion  562 . The tapered portion  562  defines four flow passages  568  and eight sealing portions  572 , each disposed adjacent to the edges of the flow passages  568 . Rather than extending through the tapered portion  562 , the illustrated flow passages  568  are recesses in the outer surface  563  that extend continuously around the outer surface  563  of the tapered portion  562 . 
     In other embodiments, the flow passages can be recesses that extend only partially around the outer surface of the tapered portion (see  FIGS. 24 and 25 , discussed in more detail herein). In yet other embodiments, the tapered portion can include any suitable combination of flow passage configurations. For example, in some embodiments, some of the flow passages can be configured to extend through the tapered portion while other flow passages can be configured to extend around the outer surface of the tapered portion. 
     Although the valve members are shown and described above as including multiple sealing portions that extend around the perimeter of the tapered portion, in other embodiments, the sealing portion does not extend around the perimeter of the tapered portion. For example,  FIG. 17  shows a perspective view of a valve member  660  according to an embodiment in which the sealing portions  672  extend continuously around the openings  669  of the flow passages  668 . Similar to the valve members described above, the valve member  660  includes a first stem portion  676 , a second stem portion  677  and a tapered portion  662 . The tapered portion  662  defines four flow passages  668  extending therethrough. Each flow passage  668  includes a first opening  669  and a second opening (not shown) disposed opposite the first opening. As described above, the first opening and the second opening of each flow passage  668  are configured to align with corresponding gas manifold flow passages and cylinder flow passages, respectively, defined by the cylinder head (not shown). 
     The tapered portion  662  includes four sealing portions  672  disposed on the outer surface  663  of the tapered portion  662 . Each sealing portion  672  includes a locus of points that extends continuously around a first opening  669 . In this arrangement, when the cylinder head assembly is in the closed configuration, the sealing portion  672  contacts a portion of the interior surface (not shown) of the cylinder head (not shown) such that the first opening  669  is fluidically isolated from its corresponding gas manifold flow passage (not shown). Although shown as including four sealing portions  672 , each extending continuously around a first opening  669 , in some embodiments, the sealing portions can extend continuously around the second opening  670 , thereby fluidically isolating the second opening from the corresponding cylinder flow passage when the cylinder head assembly is in the closed configuration. In other embodiments, a valve member can include sealing portions extending around both the first opening  669  and the second opening  670 . 
       FIG. 18  shows a perspective view of a valve member  760  according to an embodiment in which the sealing portions  772  are two-dimensional. As illustrated, the valve member  760  includes a tapered portion  772 , a first stem portion  776  and a second stem portion  777 . As described above, the tapered portion includes four flow passages  768  therethrough. The tapered portion also includes four sealing portions  772  each disposed adjacent each flow passage  768  and extending continuously around a first opening  769  of the flow passages  768 . The sealing portions  772  differ from the sealing portions  672  described above, in that the sealing portions  772  have a width X as measured along the longitudinal axis Lv of the valve member  760 . 
       FIG. 19  shows a perspective view of a valve member  860  according to an embodiment in which the sealing portions  872  extend around the perimeter of the tapered portion  862  and extend around the first openings  869 . Similar to the valve members described above, the valve member  860  includes a first stem portion  876 , a second stem portion  877  and a tapered portion  862 . The tapered portion  862  defines four flow passages  868  extending therethrough. Each flow passage  868  includes a first opening  869  and a second opening (not shown) disposed opposite the first opening. The tapered portion  862  includes sealing portions  872  disposed on the outer surface  863  of the tapered portion  862 . As shown, each sealing portion  872  extends around the perimeter of the tapered portion  862  and extends around the first openings  869 . In some embodiments, the sealing portions can comprise the entire space between adjacent openings. 
     As discussed above, in some embodiments, a cylinder head can include one or more valve inserts disposed within the valve pocket. For example,  FIGS. 20 and 21  show a portion of a cylinder head assembly  930  having a valve insert  942  disposed within the valve pocket  938 . The illustrated cylinder head assembly  930  includes a cylinder head  932  and a valve member  960 . The cylinder head  932  has a first exterior surface  935  configured to be coupled to a cylinder (not shown) and a second exterior surface  936  configured to be coupled to a gas manifold (not shown). The cylinder head  932  has an interior surface  934  that defines a valve pocket  938  having a longitudinal axis Lp. The cylinder head  932  also defines four cylinder flow passages  948  and four gas manifold flow passages  944 , configured in a manner similar to those described above. 
     The valve insert  942  includes a sealing portion  940  and defines four insert flow passages  945  that extend through the valve insert. The valve insert  942  is disposed within the valve pocket  938  such that a first portion of each insert flow passage  945  is aligned with one of the gas manifold flow passages  944  and a second portion of each insert flow passage  945  is aligned with one of the cylinder flow passages  948 . 
     The valve member  960  has a tapered portion  962 , a first stem portion  976  and a second stem portion  977 . The tapered portion  962  has an outer surface  963  and defines four flow passages  968  extending therethrough, as described above. The tapered portion  962  also includes multiple sealing portions (not shown) each of which is disposed adjacent one of the flow passages  968 . The sealing portions can be of any type discussed above. The valve member  960  is disposed within the valve pocket  938  such that the tapered portion  962  of the valve member  960  can be moved along a longitudinal axis Lv of the valve member  960  within the valve pocket  938  between an opened position ( FIGS. 20 and 21 ) and a closed position (not shown). When in the opened position, the valve member  960  is positioned within the valve pocket  938  such that each flow passage  968  is aligned with and in fluid communication with one of the insert flow passages  945 , one of the cylinder flow passages  948  and one of the gas manifold flow passages  944 . Conversely, when in the closed position, the valve member  960  is positioned within the valve pocket  938  such that the sealing portions are in contact with the sealing portion  940  of the valve insert  942 . In this manner, the flow passages  968  are fluidically isolated from the cylinder flow passages  948  and/or the gas manifold flow passages  944 . 
     As shown in  FIG. 21 , the valve pocket  938 , the valve insert  942  and the valve member  960  all have a circular cross-sectional shape. In other embodiments, the valve pocket can have a non-circular cross-sectional shape. For example, in some embodiments, the valve pocket can include an alignment surface configured to mate with a corresponding alignment surface on the valve insert. Such an arrangement may be used, for example, to ensure that the valve insert is properly aligned (i.e., that the insert flow passages  945  are rotationally aligned to be in fluid communication with the gas manifold flow passages  944  and the cylinder flow passages  948 ) when the valve insert  942  is installed into the valve pocket  938 . In other embodiments, the valve pocket, the valve insert and/or the valve member can have any suitable cross-sectional shape. 
     The valve insert  942  can be coupled within the valve pocket  938  using any suitable method. For example, in some embodiments, the valve insert can have an interference fit with the valve pocket. In other embodiments, the valve insert can be secured within the valve pocket by a weld, by a threaded coupling arrangement, by peening a surface of the valve pocket to secure the valve insert, or the like. 
       FIG. 22  shows a cross-sectional view of a portion of a cylinder head assembly  1030  according to an embodiment that includes multiple valve inserts  1042 . Although  FIG. 22  only shows one half of the cylinder head assembly  1030 , one skilled in the art should recognize that the cylinder head assembly is generally symmetrical about the longitudinal axis Lp of the valve pocket, and is similar to the cylinder head assemblies shown and described above. The illustrated cylinder head assembly  1030  includes a cylinder head  1032  and a valve member  1060 . As described above, the cylinder head  1032  can be coupled to at least one cylinder and at least one gas manifold. The cylinder head  1032  has an interior surface  1034  that defines a valve pocket  1038  having a longitudinal axis Lp. The cylinder head  1032  also defines three cylinder flow passages (not shown) and three gas manifold flow passages  1044 . 
     As shown, the valve pocket  1038  includes several discontinuous, stepped portions. Each stepped portion includes a surface substantially parallel to the longitudinal axis Lp, through which one of the gas manifold passages  1044  extends. A valve insert  1042  is disposed within each discontinuous, stepped portion of the valve pocket  1038  such that a sealing portion  1040  of the valve insert  1042  is adjacent the tapered portions  1061  of the valve member  1060 . In this arrangement, the valve inserts  1042  are not disposed about the gas manifold flow passages  1044  and therefore do not have an insert flow passage of the type described above. 
     The valve member  1060  has a central portion  1062 , a first stem portion  1076  and a second stem portion  1077 . The central portion  1062  includes three tapered portions  1061 , each disposed adjacent a surface that is substantially parallel to the longitudinal axis of the valve member Lv. The central portion  1062  defines three flow passages  1068  extending therethrough and having an opening disposed on one of the tapered portions  1061 . Each tapered portion  1061  includes one or more sealing portions of any type discussed above. The valve member  1060  is disposed within the valve pocket  1038  such that the central portion  1062  of the valve member  1060  can be moved along a longitudinal axis Lv of the valve member  1060  within the valve pocket  1038  between an opened position (shown in  FIG. 22 ) and a closed position (not shown). When in the opened position, the valve member  1060  is positioned within the valve pocket  1038  such that each flow passage  1068  is aligned with and in fluid communication with one of the cylinder flow passages (not shown) and one of the gas manifold flow passages  1044 . Conversely, when in the closed position, the valve member  1060  is positioned within the valve pocket  1038  such that the sealing portions on the tapered portions  1061  are in contact with the sealing portion  1040  of the corresponding valve insert  1042 . In this manner, the flow passages  1068  are fluidically isolated from the gas manifold flow passages  1044  and/or the cylinder flow passages (not shown). 
     Although the cylinder heads are shown and described above as having the same number of gas manifold flow passages and cylinder flow passages, in some embodiments, a cylinder head can have fewer gas manifold flow passages than cylinder flow passages or vice versa. For example,  FIG. 23  shows a cylinder head assembly  1160  according to an embodiment that includes a four cylinder flow passages  1148  by only one gas manifold flow passage  1144 . The illustrated cylinder head assembly  1130  includes a cylinder head  1132  and a valve member  1160 . The cylinder head  1132  has a first exterior surface  1135  configured to be coupled to a cylinder (not shown) and a second exterior surface  1136  configured to be coupled to a gas manifold (not shown). The cylinder head  1132  has an interior surface  1134  that defines a valve pocket  1138  within which the valve member  1160  is disposed. As shown, the cylinder head  1132  defines four cylinder flow passages  1148  and one gas manifold flow passage  1144 , configured similar to those described above. 
     The valve member  1160  has a tapered portion  1162 , a first stem portion  1176  and a second stem portion  1177 . The tapered portion  1162  defines four flow passages  1168  extending therethrough, as described above. The tapered portion  1162  also includes multiple sealing portions each of which is disposed adjacent one of the flow passages  1168 . The sealing portions can be of any type discussed above. 
     The cylinder head assembly  1130  differs from those described above in that when the cylinder head assembly  1130  is in the closed configuration (see  FIG. 23 ), the flow passages  1168  are not fluidically isolated from the gas manifold flow passage  1144 . Rather, the flow passages  1168  are only isolated from the cylinder flow passages  1148 , in a manner described above. 
     Although the engines are shown and described as having a cylinder coupled to a first surface of a cylinder head and a gas manifold coupled to a second surface of a cylinder head, wherein the second surface is opposite the first surface thereby producing a “straight flow” configuration, the cylinder and the gas manifold can be arranged in any suitable configuration. For example, in some instances, it may be desirable for the gas manifold to be coupled to a side surface  1236  of a the cylinder head.  FIGS. 24 and 25  show a cylinder head assembly  1230  according to an embodiment in which the cylinder flow passages  1248  are substantially normal to the gas manifold flow passages  1244 . In this manner, a gas manifold (not shown) can be mounted on a side surface  1236  of the cylinder head  1232 . 
     The illustrated cylinder head assembly  1230  includes a cylinder head  1232  and a valve member  1260 . The cylinder head  1232  has a bottom surface  1235  configured to be coupled to a cylinder (not shown) and a side surface  1236  configured to be coupled to a gas manifold (not shown). The side surface  1236  is disposed adjacent to and substantially normal to the bottom surface  1235 . In other embodiments, the side surface can be angularly offset from the bottom surface by an angle other than 90 degrees. The cylinder head  1232  has an interior surface  1234  that defines a valve pocket  1238  having a longitudinal axis Lp. The cylinder head  1232  also defines four cylinder flow passages  1248  and four gas manifold flow passages  1244 . The cylinder flow passages  1248  and the gas manifold flow passages  1244  differ from those previously discussed in that the cylinder flow passages  1248  are substantially normal to the gas manifold flow passages  1244 . 
     The valve member  1260  has a tapered portion  1262 , a first stem portion  1276  and a second stem portion  1277 . The tapered portion  1262  includes an outer surface  1263  and defines four flow passages  1268 . The flow passages  1268  are not lumens that extend through the tapered portion  1262 , but rather are recesses in the tapered portion  1262  that extend partially around the outer surface  1263  of the tapered portion  1262 . The flow passages  1268  include a curved surface  1271  to direct the flow of gas through the valve member  1260  in a manner that minimizes the flow losses. In some embodiments, a surface  1271  of the flow passages  1268  can be configured to produce a desired flow characteristic, such as, for example, a rotational flow pattern in the incoming and/or outgoing flow. 
     The tapered portion  1262  also includes multiple sealing portions (not shown) each of which is disposed adjacent one of the flow passages  1268 . The sealing portions can be of any type discussed above. The valve member  1260  is disposed within the valve pocket  1238  such that the tapered portion  1262  of the valve member  1260  can be moved along a longitudinal axis Lv of the valve member  1260  within the valve pocket  1238  between an opened position ( FIGS. 24 and 25 ) and a closed position (not shown), as described above. 
     Although the flow passages defined by the valve member have been shown and described as being substantially parallel to each other and substantially normal to the longitudinal axis of the valve member, in some embodiments the flow passages can be angularly offset from each other and/or can be offset from the longitudinal axis of the valve member by an angle other than 90 degrees. Such an offset may be desirable, for example, to produce a desired flow characteristic, such as, for example, swirl or tumble pattern in the incoming and/or outgoing flow.  FIG. 26  shows a cross-sectional view of a valve member  1360  according to an embodiment in which the flow passages  1368  are angularly offset from each other and are not normal to the longitudinal axis Lv. Similar to the valve members described above, the valve member  1360  includes a tapered portion  1362  that defines four flow passages  1368  extending therethrough. Each flow passage  1368  has a longitudinal axis Lf. As illustrated, the longitudinal axes Lf are angularly offset from each other. Moreover, the longitudinal axes Lf are offset from the longitudinal axis of the valve member by an angle other than 90 degrees. 
     Although the flow passages  1368  are shown and described as having a linear shape and defining a longitudinal axis Lf, in other embodiments, the flow passages can have a curved shape characterized by a curved centerline. As described above, flow passages can be configured to have a curved shape to produce a desired flow characteristic in the gas entering and/or exiting the cylinder. 
       FIG. 27  is a perspective view of a valve member  1460  according to an embodiment that includes a one-dimensional tapered portion  1462 . The illustrated valve member  1460  includes a tapered portion  1462  that defines three flow passages  1468  extending therethrough. The tapered portion includes three sealing portions  1472 , each of which is disposed adjacent one of the flow passages  1468  and extends continuously around an opening of the flow passage  1468 . 
     The tapered portion  1462  of the valve member  1460  has a width W measured along a first axis Y that is normal to a longitudinal axis Lv of the tapered portion  1462 . Similarly, the tapered portion  1462  has a thickness T measured along a second axis Z that is normal to both the longitudinal axis Lv and the first axis Y. The tapered portion  1462  has a one-dimensional taper characterized by a linear change in the thickness T. Conversely, the width W remains constant along the longitudinal axis Lv. As shown, the thickness of the tapered portion  1462  increases from a value of T 1  at one end of the tapered portion  1462  to a value of T 2  at the opposite end of the tapered portion  1462 . The change in thickness along the longitudinal axis Lv defines a taper angle α. 
     Although the valve members have been shown and described as including at least one tapered portion that includes one or more sealing portions, in some embodiments, a valve member can include a sealing portion disposed on a non-tapered portion of the valve member. In other embodiments, a valve member can be devoid of a tapered portion.  FIG. 28  is a front view of a valve member  1560  that is devoid of a tapered portion. The illustrated valve member  1560  has a central portion  1562 , a first stem portion  1576  and a second stem portion  1577 . The central portion  1562  has an outer surface  1563  and defines three flow passages  1568  extending continuously around the outer surface  1563  of the central portion  1562 , as described above. The central portion  1562  also includes multiple sealing portions  1572  each of which is disposed adjacent one of the flow passages  1568  and extends continuously around the perimeter of the central portion  1562 . 
     In a similar manner as described above, the valve member  1560  is disposed within a valve pocket (not shown) such that the central portion  1562  of the valve member  1560  can be moved along a longitudinal axis Lv of the valve member  1560  within the valve pocket between an opened position and a closed position. When in the opened position, the valve member  1560  is positioned within the valve pocket such that each flow passage  1568  is aligned with and in fluid communication with the corresponding cylinder flow passages and gas manifold flow passages (not shown). Conversely, when in the closed position, the valve member  1560  is positioned within the valve pocket such that the sealing portions  1572  are in contact with a portion of the interior surface of the cylinder head, thereby are fluidically isolating the flow passages  1568 . 
     As described above, the sealing portions  1572  can be, for example, sealing rings that are disposed within a groove defined by the outer surface of the valve member. Such sealing rings can be, for example, spring-loaded rings, which are configured to expand radially, thereby ensuring contact with the interior surface of the cylinder head when the valve member  1560  is in the closed position. 
     Conversely,  FIGS. 29 and 30  show portion of a cylinder head assembly  1630  that includes multiple 90 degree tapered portions  1631  in a first and second configuration, respectively. Although  FIGS. 29 and 30  only show one half of the cylinder head assembly  1630 , one skilled in the art should recognize that the cylinder head assembly is generally symmetrical about the longitudinal axis Lp of the valve pocket, and is similar to the cylinder head assemblies shown and described above. The illustrated cylinder head assembly  1630  includes a cylinder head  1632  and a valve member  1660 . The cylinder head  1632  has an interior surface  1634  that defines a valve pocket  1638  having a longitudinal axis Lp and several discontinuous, stepped portions. The cylinder head  1632  also defines three cylinder flow passages (not shown) and three gas manifold flow passages  1644 . 
     The valve member  1660  has a central portion  1662 , a first stem portion  1676  and a second stem portion  1677 . The central portion  1662  includes three tapered portions  1661  and three non-tapered portions  1667 . The tapered portions  1661  each have a taper angle of 90 degrees (i.e., substantially normal to the longitudinal axis Lv). Each tapered portion  1661  is disposed adjacent one of the non-tapered portions  1667 . The central portion  1662  defines three flow passages  1668  extending therethrough and having an opening disposed on one of the non-tapered portions  1667 . Each tapered portion  1661  includes a sealing portion that extends around the perimeter of the outer surface of the valve member  1660 . 
     The valve member  1660  is disposed within the valve pocket  1638  such that the central portion  1662  of the valve member  1660  can be moved along a longitudinal axis Lv of the valve member  1660  within the valve pocket  1638  between an opened position (shown in  FIG. 29 ) and a closed position (shown in  FIG. 30 ). When in the opened position, the valve member  1660  is positioned within the valve pocket  1638  such that each flow passage  1668  is aligned with and in fluid communication with one of the cylinder flow passages (not shown) and one of the gas manifold flow passages  1644 . Conversely, when in the closed position, the valve member  1660  is positioned within the valve pocket  1638  such that the sealing portions on the tapered portions  1661  are in contact with a corresponding sealing portion  1640  defined by the valve pocket  1638 . In this manner, the flow passages  1668  are fluidically isolated from the gas manifold flow passages  1644  and/or the cylinder flow passages (not shown). 
     Although some of the valve members are shown and described as including a first stem portion configured to engage a camshaft and a second stem portion configured to engage a spring, in some embodiments, a valve member can include a first stem portion configured to engage a biasing member and a second stem portion configured to engage an actuator. In other embodiments, an engine can include two camshafts, each configured to engage one of the stem portions of the valve member. In this manner, the valve member can be biased in the closed position by a valve lobe on the camshaft rather than a spring. In yet other embodiments, an engine can include one camshaft and one actuator, such as, for example, a pneumatic actuator, a hydraulic actuator, an electronic solenoid actuator or the like. 
       FIG. 31  is a top view of a portion of an engine  1700  according to an embodiment that includes both camshafts  1714  and solenoid actuators  1716  configured to move the valve member  1760 . The engine  1700  includes a cylinder  1703 , a cylinder head assembly  1730  and a gas manifold (not shown). The cylinder head assembly  1730  includes a cylinder head  1732 , an intake valve member  1760 I and an exhaust valve member  1760 E. The cylinder head  1732  can include any combination of the features discussed above, such as, for example, an intake valve pocket, an exhaust valve pocket, multiple cylinder flow passages, at least one manifold flow passage and the like. 
     The intake valve member  1760 I has tapered portion  1762 I, a first stem portion  1776 I and a second stem portion  1777 I. The first stem portion  1776 I has a first end  1778 I and a second end  1779 I. Similarly, the second stem portion  1777 I has a first end  1792 I and a second end  1793 I. The first end  1778 I of the first stem portion  1776 I is coupled to the tapered portion  1762 I. The second end  1779 I of the first stem portion  1776 I includes a roller-type follower  1790 I configured to engage an intake valve lobe  1715 I of an intake camshaft  1714 I. The first end  1792 I of the second stem portion  1777 I is coupled to the tapered portion  1762 I. The second end  1793 I of the second stem portion  1777 I is coupled to an actuator linkage  1796 I, which is coupled a solenoid actuator  1716 I. 
     Similarly, the exhaust valve member  1760 E has tapered portion  1762 E, a first stem portion  1776 E and a second stem portion  1777 E. A first end  1778 E of the first stem portion  1776 E is coupled to the tapered portion  1762 E. A second end  1779 E of the first stem portion  1776 E includes a roller-type follower  1790 E configured to engage an exhaust valve lobe  1715 E of an exhaust camshaft  1714 E. A first end  1792 E of the second stem portion  1777 E is coupled to the tapered portion  1762 E. A second end  1793 E of the second stem portion  1777 E is coupled to an actuator linkage  1796 E, which is coupled a solenoid actuator  1716 E. 
     In this arrangement, the valve members  1760 I,  1760 E can be moved by the intake valve lobe  1715 I and the exhaust valve lobe  1715 E, respectively, as described above. Additionally, the solenoid actuators  1716 I,  1716 E can supply a biasing force to bias the valve members  1760 I,  1760 E in the closed position, as indicated by the arrows F (intake) and J (exhaust). Moreover, in some embodiments, the solenoid actuators  1716 I,  1716 E can be used to override the standard valve timing as prescribed by the valve lobes  1715 I,  1715 E, thereby allowing the valves  1760 I,  1760 E to remain open for a greater duration (as a function of crank angle and/or time). 
     Although the engine  1700  is shown and described as including a solenoid actuator  1716  and a camshaft  1714  for controlling the movement of the valve members  1760 , in other embodiments, an engine can include only a solenoid actuator for controlling the movement of each valve member. In such an arrangement, the absence of a camshaft allows the valve members to be opened and/or closed in any number of ways to improve engine performance. For example, as discussed in more detail herein, in some embodiments the intake and/or exhaust valve members can be cycled opened and closed multiple times during an engine cycle (i.e., 720 crank degrees for a four stroke engine). In other embodiments, the intake and/or exhaust valve members can be held in a closed position throughout an entire engine cycle. 
     The cylinder head assemblies shown and described above are particularly well suited for camless actuation and/or actuation at any point in the engine operating cycle. More specifically, as previously discussed, because the valve members shown and described above do not extend into the combustion chamber when in their opened position, they will not contact the piston at any time during engine operation. Accordingly, the intake and/or exhaust valve events (i.e., the point at which the valves open and/or close as a function of the angular position of the crankshaft) can be configured independently from the position of the piston (i.e., without considering valve-to-piston contact as a limiting factor). For example, in some embodiments, the intake valve member and/or the exhaust valve member can be fully opened when the piston is at top dead center (TDC). 
     Moreover, the valve members shown and described above can be actuated with relatively little power during engine operation, because the opening of the valve members is not opposed by cylinder pressure, the stroke of the valve members is relatively low and/or the valve springs opposing the opening of the valves can have relatively low biasing force. For example, as discussed above, the stroke of the valve members can be reduced by including multiple flow passages therein and reducing the spacing between the flow passages. In some embodiments, the stroke of a valve member can be 2.3 mm (0.090 in.). 
     In addition to directly reducing the power required to open the valve member, reducing the stroke of the valve member can also indirectly reduce the power requirements by allowing the use of valve springs having a relatively low spring force. In some embodiments, the spring force can be selected to ensure that a portion of the valve member remains in contact with the actuator during valve operation and/or to ensure that the valve member does not repeatedly oscillate along its longitudinal axis when opening and/or closing. Said another way, the magnitude of the spring force can be selected to prevent valve “bounce” during operation. In some embodiments, reducing the stroke of the valve member can allow for the valve member to be opened and/or closed with reduced velocity, acceleration and jerk (i.e., the first derivative of the acceleration) profiles, thereby minimizing the impact forces and/or the tendency for the valve member to bounce during operation. As a result, some embodiments, the valve springs can be configured to have a relatively low spring force. For example, in some embodiments, a valve spring can be configured to exert a spring force of 110 N (50 lbf) when the valve member is both in the closed position and the opened position. 
     As a result of the reduced power required to actuate the valve members  1760 I,  1760 E, in some embodiments, the solenoid actuators  1716 I,  1716 E can be 12 volt actuators requiring relatively low current. For example, in some embodiments, the solenoid actuators can operate on 12 volts with a current draw during valve opening of between 14 and 15 amperes of current. In other embodiments, the solenoid actuators can be 12 volt actuators configured to operate on a high voltage and/or current during the initial valve member opening event and a low voltage and/or current when holding the valve member open. For example, in some embodiments, the solenoid actuators can operate on a “peak and hold” cycle that provides an initial voltage of between 70 and 90 volts during the first 100 microseconds of the valve opening event. 
     In addition to reducing engine parasitic losses, the reduced power requirements and/or reduced valve member stroke also allow greater flexibility in shaping the valve events. For example, in some embodiments the valve members can be configured to open and/or close such that the flow area through the valve member as a function of the crankshaft position approximates a square wave. 
     As described above, in some embodiments, the intake valve member and/or the exhaust valve member can be held open for longer durations, opened and closed multiple times during an engine cycle and the like.  FIG. 32  is a schematic of a portion of an engine  1800  according to an embodiment. The engine  1800  includes an engine block  1802  defining two cylinders  1803 . The cylinders  1803  can be, for example, two cylinders of a four cylinder engine. A reciprocating piston  1804  is disposed within each cylinder  1803 , as described above. A cylinder head  1830  is coupled to the engine block  1802 . Similar to the cylinder head assemblies described above, the cylinder head  1830  includes two electronically actuated intake valves  1860 I and two electronically actuated exhaust valves  1860 E. The intake valves  1860 I are configured to control the flow of gas between an intake manifold  1810 I and each cylinder  1803 . Similarly, the exhaust valves  1860 E control the exchange of gas between an exhaust manifold  1810 E and each cylinder. 
     The engine  1800  includes an electronic control unit (ECU)  1896  in communication with each of the intake valves  1860 I and the exhaust valves  1860 E. The ECU is processor of the type known in the art configured to receive input from various sensors, determine the desired engine operating conditions and convey signals to various actuators to control the engine accordingly. In the illustrated embodiment, the ECU  1896  is configured determine the appropriate valve events and provide an electronic signal to each of the valves  1860 I,  1860 E so that the valves open and close as desired. 
     The ECU  1896  can be, for example, a commercially-available processing device configured to perform one or more specific tasks related to controlling the engine  1800 . For example, the ECU  1896  can include a microprocessor and a memory device. The microprocessor can be, for example, an application-specific integrated circuit (ASIC) or a combination of ASICs, which are designed to perform one or more specific functions. In yet other embodiments, the microprocessor can be an analog or digital circuit, or a combination of multiple circuits. The memory device can include, for example, a read only memory (ROM) component, a random access memory (RAM) component, electronically programmable read only memory (EPROM), erasable electronically programmable read only memory (EEPROM), and/or flash memory. 
     Although the engine  1800  is illustrated and described as including an ECU  1896 , in some embodiments, an engine  1800  can include software in the form of processor-readable code instructing a processor to perform the functions described herein. In other embodiments, an engine  1800  can include firmware that performs the functions described herein. 
       FIG. 33  is a schematic of a portion of the engine  1800  operating in a “cylinder deactivation” mode. Cylinder deactivation is a method of improving the overall efficiency of an engine by temporarily deactivating the combustion event in one or more cylinders during periods in which the engine is operating at reduced loads (i.e. when the engine is producing a relatively low amount of torque and/or power), such as, for example, when a vehicle is operating at highway speeds. Operating at reduced loads is inherently inefficient due to, among other things, the high pumping losses associated with throttling the intake air. In such instances, the overall engine efficiency can be improved by deactivating the combustion event in one or more cylinders, which requires the remaining cylinders to operate at a higher load and therefore with less throttling of the intake air, thereby reducing the pumping losses. 
     When the engine  1800  is operating in the cylinder deactivation mode, cylinder  1803 A, which can be, for example cylinder #4 of a four cylinder engine, is the firing cylinder, operating on a standard four stroke combustion cycle. Conversely, cylinder  1803 B, which can be, for example, cylinder #3 of a four cylinder engine, is the deactivated cylinder. As shown in  FIG. 33 , the engine  1800  is configured such that the piston  1804 A within the firing cylinder  1803 A is moving downwardly from top dead center (TDC) towards bottom dead center (BDC) on the intake stroke, as indicated by arrow AA. During the intake stroke, the intake valve  1860 IA is opened thereby allowing air or an air/fuel mixture to flow from the intake manifold  1810 I into the cylinder  1803 A, as indicated by arrow N. The exhaust valve  1860 EA is closed, such that the cylinder  1803 A is fluidically isolated from the exhaust manifold  1810 E. 
     Conversely, the piston  1804 B within the deactivated cylinder  1803 B is moving upwardly from BDC towards TDC, as indicated by arrow BB. As illustrated, the intake valve  1860 IB is opened thereby allowing air to flow from the cylinder  1803 B into the intake manifold  1810 I, as indicated by arrow P. The exhaust valve  1860 EB is closed such that the cylinder  1803 B is fluidically isolated from the exhaust manifold  1810 E. In this manner, the engine  1800  is configured so that cylinder  1803 B operates to pump air contained therein into the intake manifold  1810 I and/or cylinder  1803 A. Said another way, cylinder  1803 B is configured to act as a supercharger. In this manner, the engine  1800  can operate in a “standard” mode, in which cylinders  1803 A and  1803 B operate as naturally aspirated cylinders to combust fuel and air, and a “pumping assist” mode, in which cylinder  1803 B is deactivated and the cylinder  1803 A operates as a boosted cylinder to combust fuel and air. 
     Although the engine  1800  is shown and described operating in a cylinder deactivation mode in which one cylinder supplies air to another cylinder, in some embodiments, an engine can operate in a cylinder deactivation mode in which both the exhaust valve and the intake valve of the non-firing cylinder remain closed throughout the entire engine cycle. In other embodiments, an engine can operate in a cylinder deactivation mode in which the intake valve and/or exhaust valve of the non-firing cylinder is held open throughout the entire engine cycle, thereby eliminating the parasitic losses associated with pumping air through the non-firing cylinder. In yet other embodiments, an engine can operate in a cylinder deactivation mode in which the non-firing cylinder is configured to absorb power from the vehicle, thereby acting as a vehicle brake. In such embodiments, for example, the exhaust valve of the non-firing cylinder can be configured to open early so that the compressed air contained therein is released without producing any expansion work. 
       FIGS. 34-36  are graphical representations of the valve events of a cylinder of a multi-cylinder engine operating in a standard four stroke combustion mode, a first exhaust gas recirculation (EGR) mode and a second EGR mode respectively. The longitudinal axes indicate the position of the piston within the cylinder in terms of the rotational position of the crankshaft. For example, the position of 0 degrees occurs when the piston is at top dead center on the firing stroke of the engine, the position of 180 degrees occurs when the piston is at bottom dead center after firing, the position of 360 degrees occurs when the piston is at top dead center on the gas exchange stroke, and so on. The regions bounded by dashed lines represent periods during which an intake valve associated with the cylinder is opened. Similarly, the regions bounded by solid lines represent the periods during which an exhaust valve associated with the cylinder is opened. 
     As shown in  FIG. 34 , when the engine is operating in a four stroke combustion mode, the compression event  1910  occurs after the gaseous mixture is drawn into the cylinder. During the compression event  1910 , both the intake and exhaust valves are closed as the piston moves upwardly towards TDC, thereby allowing the gaseous mixture contained in the cylinder to be compressed by the motion of the piston. At a suitable point, such as, for example −10 degrees, the combustion event  1915  begins. At a suitable point as the piston moves downwardly, such as, for example, 120 degrees, the exhaust valve open event  1920  begins. In some embodiments, the exhaust valve open event  1920  continues until the piston has reached TDC and has begun moving downwardly. Moreover, as shown in  FIG. 34 , the intake valve open event  1925  can begin before the exhaust valve open event  1920  ends. In some embodiments, for example, the intake valve open event  1925  can begin at 340 degrees and the exhaust valve open event  1920  can end at 390 degrees, thereby resulting in an overlap duration of 50 degrees. At a suitable point, such as, for example, 600 degrees, the intake valve open event  1925  ends and a new cycle begins. 
     In some embodiments, a predetermined amount of exhaust gas is conveyed from the exhaust manifold to the intake manifold via an exhaust gas recirculation (EGR) valve. In some embodiments, the EGR valve is controlled to ensure that precise amounts of exhaust gas are conveyed to the intake manifold. 
     As shown in  FIG. 35 , when the engine is operating in the first EGR mode, the intake valve associated with the cylinder is configured to convey exhaust gas from the cylinder directly into the intake manifold (not shown in  FIG. 35 ), thereby eliminating the need for a separate EGR valve. As shown, the compression event  1910 ′ occurs after the gaseous mixture is drawn into the cylinder. During the compression event  1910 ′, both the intake and exhaust valves are closed as the piston moves upwardly towards TDC, thereby allowing the gaseous mixture contained in the cylinder to be compressed by the motion of the piston. As described above, at a suitable point, the combustion event  1915 ′ begins. Similarly, at a suitable point the exhaust valve open event  1920 ′ begins. At a suitable point during the exhaust valve event  1920 ′, such as, for example, at 190 degrees, the first intake valve open event  1950  occurs. Because the first intake valve open event  1950  can be configured to occur when the pressure of the exhaust gas within the cylinder is greater than the pressure in the intake manifold, a portion of the exhaust gas will flow from the cylinder into the intake manifold. In this manner, exhaust gas can be conveyed directly into the intake manifold via the intake valve. The amount of exhaust gas flow can be controlled, for example, by varying the duration of the first intake valve open event  1950 , adjusting the point at which the first intake valve open event  1950  occurs and/or varying the stroke of the intake valve during the first intake valve open event  1950 . 
     As shown in  FIG. 35 , the second intake valve open event  1925 ′ can begin before the exhaust valve open event  1920 ′ ends. As described above, at suitable points, the first intake valve open event  1950  ends, the second intake valve open event  1925 ′ ends and a new cycle begins. 
     As shown in  FIG. 36 , when the engine is operating in the second EGR mode, the exhaust valve associated with the cylinder is configured to convey exhaust gas from the exhaust manifold (not shown) directly into the cylinder (not shown in  FIG. 35 ), thereby eliminating the need for a separate EGR valve. As shown, the compression event  1910 ″ occurs after the gaseous mixture is drawn into the cylinder. During the compression event  1910 ″, both the intake and exhaust valves are closed as the piston moves upwardly towards TDC, thereby allowing the gaseous mixture contained in the cylinder to be compressed by the motion of the piston. As described above, at a suitable point, the combustion event  1915 ″ begins. Similarly, at a suitable point the first exhaust valve open event  1920 ″ begins. 
     As described above, the intake valve open event  1925 ″ can begin before the first exhaust valve open event  1920 ″ ends. At a suitable point during the intake valve open event  1925 ″, such as, for example, at 500 degrees, the second exhaust valve open event  1960  occurs. Because the second exhaust valve open event  1960  can be configured to occur when the pressure of the exhaust gas within the exhaust manifold is greater than the pressure in the cylinder, a portion of the exhaust gas will flow from the exhaust manifold into the cylinder. In this manner, exhaust gas can be conveyed directly into the cylinder via the exhaust valve. The amount of exhaust gas flow into the cylinder can be controlled, for example, by varying the duration of the second exhaust valve open event  1960 , adjusting the point at which the second exhaust valve open event  1960  occurs and/or varying the stroke of the exhaust valve during the second exhaust valve open event  1960 . As described above, at suitable points, the second exhaust valve open event  1970  ends, the intake valve open event  1925 ″ ends and a new cycle begins. 
     Although the valve events are represented as square waves, in other embodiments, the valve events can have any suitable shape. For example, in some embodiments the valve events can be configured to as sinusoidal waves. In this manner, the acceleration of the valve member can be controlled to minimize the likelihood of valve bounce during the opening and/or closing of the valve. 
     In addition to allowing improvements in engine performance, the arrangement of the valve members shown and described above also results in improvements in the assembly, repair, replacement and/or adjustment of the valve members. For example, as previously discussed with reference to  FIG. 5  and as shown in  FIG. 37  the end plate  323  is removably coupled to the cylinder head  332  via cap screws  317 , thereby allowing access to the spring  318  and the valve member  360  for assembly, repair, replacement and/or adjustment. Because the valve member  360  does not extend below the first surface  335  of the cylinder head (i.e., the valve member  360  does not protrude into the cylinder  303 ), the valve member  360  can be installed and/or removed without removing the cylinder head assembly  330  from the cylinder  303 . Moreover, because the tapered portion  362  of the valve member  360  is disposed within the valve pocket  338  such that the width and/or thickness of the valve member  360  increases away from the camshaft  314  (e.g., in the direction indicated by arrow C in  FIG. 5 ), the valve member  360  can be removed without removing the camshaft  314  and/or any of the linkages (i.e., tappets) that can be disposed between the camshaft  314  and the valve member  360 . Additionally, the valve member  360  can be removed without removing the gas manifold  310 . For example, in some embodiments, a user can remove the valve member  360  by moving the end plate  323  such that the valve pocket  338  is exposed, removing the spring  318 , removing the alignment key  398  from the keyway  399  and sliding the valve member  360  out of the valve pocket  338 . Similar procedures can be followed to replace the spring  318 , which may be desirable, for example, to adjust the biasing force applied to the first stem portion  377  of the valve member  360 . 
     Similarly, an end plate  322  (see  FIG. 5 ) is removably coupled to the cylinder head  332  to allow access to the camshaft  314  and the first stem portion  376  for assembly, repair and/or adjustment. For example, as discussed in more detail herein, in some embodiments, a valve member can include an adjustable tappet (not shown) configured to provide a predetermined clearance between the valve lobe of the camshaft and the first stem portion when the cylinder head is in the closed configuration. In such arrangements, a user can remove the end plate  322  to access the tappet for adjustment. In other embodiments, the camshaft is disposed within a separate cam box (not shown) that is removably coupled to the cylinder head. 
       FIG. 38  is a flow chart illustrating a method  2000  for assembling an engine according to an embodiment. The illustrated method includes coupling a cylinder head to an engine block,  2002 . As described above, in some embodiments, the cylinder head can be coupled to the engine block using cylinder head bolts. In other embodiments, the cylinder head and the engine block can be constructed monolithically. In such embodiments, the cylinder head is coupled to the engine block during the casting process. At  2004 , a camshaft is then installed into the engine. 
     The method then includes moving a valve member, of the type shown and described above, into a valve pocket defined by the cylinder head,  2006 . As previously discussed, in some embodiments, the valve member can be installed such that a first stem portion of the valve member is adjacent to and engages a valve lobe of the camshaft. Once the valve member is disposed within the valve pocket, a biasing member is disposed adjacent a second stem portion of the valve member,  2008 , and a first end plate is coupled to the cylinder head, such that a portion of the biasing member engages the first end plate,  2010 . In this manner, the biasing member is retained in place in a partially compressed (i.e., preloaded) configuration. The amount of biasing member preload can be adjusted by adding and/or removing spacers between the first end plate and the biasing member. 
     Because the biasing member can be configured to have a relatively low preload force, in some embodiments, the first end plate can be coupled to the cylinder head without using a spring compressor. In other embodiments, the cap screws securing the first end plate to the cylinder head can have a predetermined length such that the first end plate can be coupled to the cylinder without using a spring compressor. 
     The illustrated method then includes adjusting a valve lash setting,  2012 . In some embodiments, the valve lash setting is adjusted by adjusting a tappet disposed between the first stem portion of the valve member and the camshaft. In other embodiments, a method does not include adjusting the valve lash setting. The method then includes coupling a second end plate to the cylinder head,  2014 , as described above. 
       FIG. 39  is a flow chart illustrating a method  2100  for replacing a valve member in an engine without removing the cylinder head according to an embodiment. The illustrated method includes moving an end plate to expose a first opening of a valve pocket defined by a cylinder head,  2102 . In some embodiments, the end plate can be removed from the cylinder head. In other embodiments, the end plate can be loosened and pivoted such that the first opening is exposed. A biasing member, which is disposed between a second end portion of the valve member and the end plate, is removed,  2104 . In this manner, the second end portion of the valve member is exposed. The valve member is then moved from within the valve pocket through the first opening,  2106 . In some embodiments, the camshaft can be rotated to assist in moving the valve member through the first opening. A replacement valve member is disposed within the valve pocket,  2108 . The biasing member is then replaced,  2110 , and the end plate is coupled to the cylinder head  2112 , as described above. 
       FIGS. 40-43  are schematic illustrations of top view of a portion of an engine  3100  having a variable travel valve actuator assembly  3200 , according to an embodiment. The engine  3100  includes an engine block (not shown in  FIGS. 40-43 ), a cylinder head  3132 , a valve  3160  and an actuator assembly  3200 . The engine block defines a cylinder  3103  (shown in dashed lines) within which a piston (not shown in  FIGS. 40-43 ) can be disposed. The cylinder head  3132  is coupled to the engine block such that a portion of the cylinder head  3132  covers the upper portion of the cylinder  3103  thereby forming a combustion chamber. The cylinder head  3132  defines a valve pocket  3138  and four cylinder flow passages (not shown in  FIGS. 40-43 ). The cylinder flow passages are in fluid communication with the valve pocket  3138  and the cylinder  3103 . In this manner, as described herein, a gas (e.g., an exhaust gas or an intake gas) can flow between a region outside of the engine  3100  and the cylinder  3103  via the cylinder head  3132 . 
     The valve  3160  has a first end portion  3176  and a second end portion  3177 , and defines four flow openings  3168  (only one of the flow openings is labeled in  FIGS. 40-43 ). The flow openings  3168  correspond to the cylinder flow passages of the cylinder head  3132 . Although the valve  3160  is shown as defining four flow openings  3168 , in other embodiments, the valve  3160  can define any number of flow openings (e.g., one, two, three, or more). In some embodiments, the valve  3160  can be a tapered valve similar to the valve  360  shown and described above. 
     The valve  3160  is movably disposed within the valve pocket  3138  of the cylinder head  3132 . More particularly, the valve  3160  can move within the valve pocket  3138  between a closed position (e.g.,  FIGS. 40 and 42 ) and multiple different opened positions (e.g.,  FIGS. 41 and 43 ). When the valve  3160  is in the closed position, each flow opening  3168  is offset (or out of alignment with) from the corresponding cylinder flow passages. Moreover, when the valve  3160  is in the closed position, at least a portion of the valve  3160  is in contact with a portion of the interior surface of the cylinder head  3132  that defines the valve pocket  3138  such that the cylinder flow passages are fluidically isolated from the cylinder  3103 . In some embodiments, the valve  3160  can include a sealing portion (not shown in  FIGS. 40-43 ), such as for example, a tapered surface, configured to engage a surface of the cylinder head  3132  to fluidically isolate the cylinder  3103  from the region outside of the engine  3100 . 
     As shown in  FIGS. 40 and 42 , when the valve  3160  is in the closed position, the first end portion  3176  of the valve is offset from an end plate  3123  by a distance d cl . A spring  3118  is disposed between the first end portion  3176  of the valve  3160  and an end plate  3123 . The spring  3118  exerts a force on the valve  3160  in the direction shown by the arrow CC in  FIG. 40  to bias the valve  3160  in the closed position. When the valve  3160  is in the closed position, the valve  3160  can be prevented from moving further in the direction shown by the arrow CC by any suitable mechanism. Such mechanisms can include, for example, mating tapered surfaces of the valve  3160  and the valve pocket  3138 , a mechanical end-stop, a magnetic device or the like. 
     As described in more detail below, the actuator assembly  3200  is configured to selectively vary the distance through which the valve  3160  travels when moving between the closed position and an opened position. Similarly stated, the valve  3160  can be moved between the closed position ( FIGS. 40 and 42 ) and any number of different opened positions.  FIG. 41  illustrates the valve  3160  in a fully opened position, or the opened position corresponding to a first configuration of the actuator assembly  3200 .  FIG. 43  illustrates the valve  3160  in a partially opened position, or the opened position corresponding to a second configuration of the actuator assembly  3200 . When the valve  3160  is in an opened position, each flow opening  3168  of the valve  3160  is at least partially aligned with the corresponding cylinder flow passages. Moreover, when the valve  3160  is in an opened position, a portion of the valve  3160  is spaced apart from the interior surface of the cylinder head  3132  that defines the valve pocket  3138  such that the cylinder flow passages are in fluid communication with the cylinder  3103 . Thus, when the valve  3160  is in an opened position, a gas (e.g., an exhaust gas or an intake gas) can flow between a region outside of the engine  3100  and the cylinder  3103  via the cylinder head  3132 . 
     As shown in  FIG. 41  when the valve is in the first opened position (i.e., the fully opened position), the first end portion  3176  of the valve is offset from the end plate  3123  by a distance d op1 . Thus, the distance through which the valve  3160  travels when moved from the closed position to the first opened position is represented by equation (1).
 
Travel 1   =d   cl   −d   op1   (1)
 
As shown in  FIG. 43  when the valve is in the second opened position (i.e., the partially opened position), the first end portion  3176  of the valve is offset from the end plate  3123  by a distance d op2 , which is greater than the distance d op1 . Thus, the distance through which the valve  3160  travels when moved from the closed position to the second opened position is less than the distance through which the valve  3160  travels when moved from the closed position to the first opened position. The distance through which the valve  3160  travels when moved from the closed position to the second opened position is represented by equation (2).
 
Travel 2   =d   cl   −d   op2   (2)
 
     The actuator assembly  3200  includes a valve actuator  3210  and a variable travel actuator  3250 . The valve actuator  3210  includes a housing  3240 , a solenoid coil  3242 , a push rod  3212  and an armature  3222 . A first end portion  3243  of the housing  3240  is movably coupled to the cylinder head  3132 . In this manner, as described in more detail below, the housing  3242  (and therefore the valve actuator  3210 ) can move relative to the cylinder head  3132 . The solenoid coil  3242  is fixedly coupled within the first end portion  3243  of the housing  3240 . Similarly stated, the solenoid coil  3242  is disposed within the housing  3240  such that movement of the solenoid coil  3242  relative to the housing  3240  is prevented. 
     The push rod  3212  has a first end portion  3213  and a second end portion  3214 . The second end portion  3214  of the push rod  3212  is disposed within the housing  3240  and is coupled to the armature  3222 . More particularly, the second end portion  3214  of the push rod  3212  is coupled to the armature  3222  such that movement of the armature  3222  results in movement of the push rod  3212 . A portion of the push rod  3212  is movably disposed within the solenoid coil  3242 . In this manner, the armature  3222  and the push rod  3212  can move relative to the solenoid coil  3242 . In use, when the solenoid coil  3242  is energized with an electrical current, a magnetic field is produced that exerts a force upon the armature  3222  in a direction shown by the arrows DD and FF in  FIGS. 41 and 43 , respectively. The magnetic force causes the armature  3222  and the push rod  3212  to move relative to the solenoid coil  3242  (and the housing  3240 ), as shown by the arrows DD and FF in  FIGS. 41 and 43 , respectively. The armature  3222  and the push rod  3212  move relative to the solenoid coil  3242  through a distance Sd (i.e., the solenoid stroke) until the armature  3222  contacts the solenoid coil  3242 . When the solenoid coil  3242  is de-energized, the armature  3222  can travel in a direction opposite the direction shown by the arrows DD and FF until the armature contacts a second end portion  4244  of the housing  4240 . In some embodiments, the valve actuator  4210  includes a biasing member configured to urge the armature  3222  into contact with the second end portion of the housing  4240 . 
     The first end portion  3213  of the push rod  3212  is disposed outside of the housing  3240 . More particularly, when the housing  3240  is coupled to the cylinder head  3132 , the first end portion  3213  of the push rod  3212  is disposed within the valve pocket  3138  adjacent the second end portion  3177  of the valve  3160 . More particularly, as shown in  FIGS. 40 and 42 , when the valve  3160  is in the closed position and the solenoid coil  3242  is not energized, the first end portion  3213  of the push rod  3212  is spaced apart from the second end portion  3177  of the valve  3160 . The distance between the first end portion  3213  of the push rod  3212  and the second end portion  3177  of the valve  3160  is referred to as the valve lash (identified as L 1  in  FIG. 40  and L 2  in  FIG. 42 ). Providing clearance (i.e., valve lash) between the push rod  3212  and the valve  3160  can ensure that the valve  3160  will be operate properly (e.g., be fully seated when in the closed position) regardless of the thermal growth of the valve train components, manufacturing tolerances of the valve train components, and/or the like. 
     In use, when the solenoid coil  3242  is energized and the push rod  3212  moves as shown by the arrow DD, the first end portion  3213  of the push rod  3212  contacts the second end portion  3177  of the valve  3160 . When the force exerted by the push rod  3212  on the valve  3160  is greater than the biasing force exerted by the spring  3118 , the valve  3160  is moved from the closed position (e.g.,  FIG. 40 ) to an opened position (e.g.,  FIG. 41 ). As described above, because the valve actuator  3210  is electrically operated, the valve  3160  can be moved between the closed position and an opened position independently from the rotational position of a camshaft or a crankshaft of the engine  3100 . 
     The variable travel actuator  3250  is configured to move the housing  3240  (and therefore, the valve actuator  3210 ) relative to the cylinder head  3132 . In this manner, as described below, the variable travel actuator  3250  can selectively vary the distance through which the valve  3160  travels when moving between the closed position and an opened position. More particularly, the valve travel is related to the solenoid stroke Sd and the valve lash as indicated by equation (3).
 
Travel= Sd−L   (3)
 
Thus, the valve travel can be adjusted by changing the solenoid stroke Sd and/or the valve lash L.
 
     As shown in  FIG. 40 , when the actuator assembly  3200  is in the first (or full opening) configuration, the housing  3240  is positioned relative to the cylinder head  3132  such that the valve lash setting has a value of L 1 . Accordingly, the travel of the valve  3160  when the actuator assembly  3200  is in the first configuration is represented by equation (4).
 
Travel 1   =Sd−L   1   =d   cl   −d   op1   (4)
 
As shown in  FIG. 42 , when the actuator assembly  3200  is in the second (or partial opening) configuration, the housing  3240  is positioned relative to the cylinder head  3132  such that the valve lash setting has a value of L 2 , which is greater than L 1 . Similarly stated, when the actuator assembly  3200  is in the second (or partial opening) configuration, the housing  3240  is moved relative to the cylinder head  3132  as shown by the arrow EE in  FIG. 42 , thereby increasing the valve lash setting to a value of L 2 . Accordingly, the travel of the valve  3160  when the actuator assembly  3200  is in the second configuration is represented by equation (5).
 
Travel 2   =Sd−L   2   =d   cl   −d   op2   (5)
 
     The variable travel actuator  3250  can include any suitable mechanism for moving the valve actuator  3210  relative to the cylinder head  3132  as shown by the arrow EE in  FIG. 42 . For example, in some embodiments, the variable travel actuator  3250  can include an electronic actuator that moves the valve actuator  3210  linearly relative to the cylinder head  3132 . Similarly stated, in some embodiments, the variable travel actuator  3250  can include an electronic actuator that translates the valve actuator  3210  relative to the cylinder head  3132 . For example, in some embodiments, the variable travel actuator  3250  can include a rack and pinion arrangement to translate the valve actuator  3210  relative to the cylinder head  3132 . In other embodiments, the variable travel actuator  3250  can rotate the valve actuator  3210  relative to the cylinder head. For example, in some embodiments, the housing  3240  can include a threaded portion configured to mate with a corresponding threaded portion in the cylinder head  3132  such that rotation of the housing  3240  relative to the cylinder head  3132  results in movement as shown by the arrow EE in  FIG. 42 . 
     As described above, the variable travel actuator  3250  varies the valve travel by selectively varying the valve lash L while maintaining a constant solenoid stroke Sd. In this manner, the electro-mechanical characteristics of the valve actuator  3210  remain substantially constant when the actuator assembly  3200  is moved between the first configuration and the second configuration. Accordingly, the current to energize the solenoid coil  3242  need not change as a function of the configuration of the actuator assembly  3200 . 
     As shown in  FIGS. 40-43 , the spring  3118  is disposed adjacent the opposite end of the valve  3160  (i.e., the first end portion  3176 ) from the actuator assembly  3200 . This arrangement allows the variable travel actuator  3250  of the actuator assembly  3200  to move the valve actuator  3210  relative to the cylinder head  3132  without changing the functional characteristics of the spring  3118 . More particularly, the variable travel actuator  3250  of the actuator assembly  3200  can move the valve actuator  3210  relative to the cylinder head  3132  without changing the length of the spring  3118  when the valve  3160  is in the closed position (i.e., the initial length of the spring  3118 ). In the illustrated embodiment, the initial length of the spring  3118  corresponds to the distance dcl between the end plate  3123  and the first end portion  3176  of the valve  3160 . By maintaining a substantially constant initial length of the spring  3118 , the variable travel actuator  3250  of the actuator assembly  3200  can move the valve actuator  3210  relative to the cylinder head  3132  without changing the biasing force exerted by the spring  3118  on the valve  3160 . Accordingly, the valve  3160  can be actuated in a repeatable and/or precise manner regardless of the configuration of the actuator assembly  3200 . 
     In addition to decreasing the valve travel, selectively increasing the lash (e.g., from L 1  to L 2 ) can result in a longer time for the valve  3160  to begin moving after the solenoid  3242  is energized. Accordingly, in some embodiments, the timing of the actuation can be adjusted and/or offset as a function of the valve lash. For example, in some embodiments, the engine  3100  can include an electronic control unit or ECU (not shown) configured to automatically adjust the actuation timing as a function of the change in valve lash (e.g., L 1  to L 2 ) when the actuation assembly  3200  is moved between the first configuration and the second configuration. In some embodiments, for example, the ECU can be configured to receive an input corresponding to the valve lash setting of the valve when the actuation assembly is in the first configuration (e.g., the full opening configuration) and adjust the actuation timing as a function of the actual change in valve lash setting. In this manner, the ECU can control the actuation timing for a particular engine, rather than based on nominal values for a general engine design. 
     Although the actuator assembly  3200  is shown as having only one partial opening configuration (e.g.,  FIGS. 42 and 43 ), the actuator assembly  3200  can be moved between the full opening configuration and any number of partial opening configurations. For example, the actuator assembly  3200  can be moved between a full opening configuration, a first partial opening configuration (in which the valve travel is approximately ¾ of the full opening valve travel), a second partial opening configuration (in which the valve travel is approximately ½ of the full opening valve travel) and a third partial opening configuration (in which the valve travel is approximately ¼ of the full opening valve travel). In another example, the actuator assembly  3200  can be moved between the full opening configuration and an infinite number of partial opening configurations. For example in some embodiments, the actuator assembly  3200  can adjust the distance between the closed position and the opened position to any value between approximately zero inches and 0.090 inches. By selectively varying the distance between the opened position and the closed position (e.g., the valve travel), the actuator assembly  3200  can accurately and/or precisely control the amount and/or flow rate of gas flow into and/or out of the cylinder  3103 . More particularly, the valve travel can be varied in conjunction with the timing and duration of the valve opening event to provide the desired gas flow characteristics as a function of the engine operating conditions (e.g., low idle, road cruising conditions or the like). In some embodiments, the control afforded by this arrangement allows the engine gas exchange process to be controlled using only the valve  3160  and the actuator assembly  3200 , thereby removing the need for a throttle valve upstream of the cylinder head  3132 . 
     Although the top view schematic illustrations shown in  FIGS. 40-43  show the valve  3160  moving between the closed position and an opened position in a direction substantially normal to a center line (not shown) of the cylinder  3103 , in other embodiments, the valve  3160  can move in any suitable direction relative to the cylinder  3103  and/or the cylinder head  3132 . For example, in some embodiments, the valve  3160  can move substantially parallel to a center line of the cylinder  3103 . In other embodiments, the valve  3160  can move in a direction non-parallel to and non-normal to a center line of the cylinder  3103 . 
     Although the variable travel actuator  3250  is shown and described above as varying the valve travel by selectively varying the valve lash L while maintaining a constant solenoid stroke Sd, in other embodiments, a variable travel actuator can vary the valve travel by selectively varying the solenoid stroke while maintaining a substantially constant valve lash setting. For example,  FIGS. 44 and 45  are schematic illustrations of top view of a portion of an engine  4100  having a variable travel valve actuator assembly  4200 , according to an embodiment. The engine  4100  includes an engine block (not shown in  FIGS. 44 and 45 ), a cylinder head  4132 , a valve  4160  and an actuator assembly  4200 . The engine block defines a cylinder  4103  (shown in dashed lines) within which a piston (not shown in  FIGS. 44 and 45 ) can be disposed. The cylinder head  4132  is coupled to the engine block such that a portion of the cylinder head  4132  covers the upper portion of the cylinder  4103  thereby forming a combustion chamber. The cylinder head  4132  defines a valve pocket  4138  and four cylinder flow passages (not shown in  FIGS. 44 and 45 ). The cylinder flow passages are in fluid communication with the valve pocket  4138  and the cylinder  4103 . In this manner, as described above, a gas (e.g., an exhaust gas or an intake gas) can flow between a region outside of the engine  4100  and the cylinder  4103  via the cylinder head  4132 . 
     The valve  4160  has a first end portion  4176  and a second end portion  4177 , and defines four flow openings  4168  (only one of the flow openings is labeled in  FIGS. 44 and 45 ). The flow openings  4168  correspond to the cylinder flow passages of the cylinder head  4132 . Although the valve  4160  is shown as defining four flow openings  4168 , in other embodiments, the valve  4160  can define any number of flow openings (e.g., one, two, three, or more). In some embodiments, the valve  4160  can be a tapered valve similar to the valve  360  shown and described above. 
     The valve  4160  is movably disposed within the valve pocket  4138  of the cylinder head  4132 . More particularly, the valve  4160  can move within the valve pocket  4138  between a closed position (as shown in  FIGS. 44 and 45 ) and multiple different opened positions (not shown in  FIGS. 44 and 45 ). When the valve  4160  is in the closed position, the cylinder flow passages are fluidically isolated from the cylinder  4103 , as described above. A spring  4118  is disposed between the first end portion  4176  of the valve  4160  and an end plate  4123 . The spring  4118  exerts a force on the valve  4160  to bias the valve  4160  in the closed position, as described above. Similar to the arrangement described above with reference to the engine  3100 , the valve  4160  can be moved between the closed position ( FIGS. 44 and 45 ) and any number of different opened positions. When the valve  4160  is in an opened position, the cylinder flow passages are in fluid communication with the cylinder  4103 . Thus, when the valve  4160  is in an opened position, a gas (e.g., an exhaust gas or an intake gas) can flow between a region outside of the engine  4100  and the cylinder  4103  via the cylinder head  4132 . 
     The actuator assembly  4200  includes a valve actuator  4210  and a variable travel actuator  4250 . The valve actuator  4210  includes a housing  4240 , a solenoid coil  4242 , a push rod  4212  and an armature  4222 . A first end portion  4243  of the housing  4240  is fixedly coupled to the cylinder head  4132 . The solenoid coil  4242  is movably disposed within the first end portion  4243  of the housing  4240 . In this manner, as described in more detail below, the solenoid coil  4242  can be selectively moved to vary the solenoid stroke, and therefore the valve travel. 
     The push rod  4212  has a first end portion  4213  and a second end portion  4214 . The second end portion  4214  of the push rod  4212  is disposed within the housing  4240  and is coupled to the armature  4222 . More particularly, the second end portion  4214  of the push rod  4212  is coupled to the armature  4222  such that movement of the armature  4222  results in movement of the push rod  4212 . A portion of the push rod  4212  is movably disposed within the solenoid coil  4242 . In this manner, the armature  4222  and the push rod  4212  can move relative to the solenoid coil  4242 . In use, when the solenoid coil  4242  is energized the armature  4222  and the push rod  4212  are moved relative to the solenoid coil  4242  (and the housing  4240 ) until the armature  4222  contacts the solenoid coil  4242 . Similarly stated, when the solenoid coil  4242  is energized the armature  4222  and the push rod  4212  move relative to the solenoid coil  4242  a distance (i.e., the solenoid stroke). When the solenoid coil  4242  is de-energized, the armature  4222  can move in an opposite direction until the armature contacts a second end portion  4244  of the housing  4240 . In some embodiments, the valve actuator  4210  includes a biasing member configured to urge the armature  4222  into contact with the second end portion of the housing  4240 . 
     The first end portion  4213  of the push rod  4212  is disposed outside of the housing  4240 . More particularly, when the housing  4240  is coupled to the cylinder head  4132 , the first end portion  4213  of the push rod  4212  is disposed within the valve pocket  4138  adjacent the second end portion  4177  of the valve  4160 . As shown in  FIGS. 44 and 45 , when the valve  4160  is in the closed position and the solenoid coil  4242  is not energized, the first end portion  4213  of the push rod  4212  is spaced apart from the second end portion  4177  of the valve  4160  by a distance L (the valve lash). In use, when the solenoid coil  4242  is energized and the push rod  4212  moves, the first end portion  4213  of the push rod  4212  contacts the second end portion  4177  of the valve  4160 . When the force exerted by the push rod  4212  on the valve  4160  is greater than the biasing force exerted by the spring  4118 , the valve  4160  is moved from the closed position (e.g.,  FIGS. 44 and 45 ) to an opened position (not shown). 
     The variable travel actuator  4250  is configured to move the solenoid coil  4242  within the housing  4240  relative to the armature  4222  and/or the push rod  4212 , as shown by the arrow HH in  FIG. 45 . In this manner, the actuator assembly  4200  can be moved between a first (or full opening) configuration, as shown in  FIG. 44 , and a second (or partial opening) configuration, as shown in  FIG. 45 . Although shown as having only one partial opening configuration, the actuator assembly  4200  can have any number of different partial opening configurations, as described above. As shown in  FIG. 44 , when the actuator assembly  4200  is in the first configuration, the armature  4222  is spaced apart from the solenoid  4242  when the solenoid is de-energized by a distance S d1  (i.e., the solenoid stroke when the actuator assembly  4200  is in the first configuration). As shown in  FIG. 45 , when the actuator assembly  4200  is in the second configuration, the armature  4222  is spaced apart from the solenoid  4242  when the solenoid is de-energized by a distance S d2  (i.e., the solenoid stroke when the actuator assembly  4200  is in the second configuration), which is less than the distance S d1 . 
     As described above, the valve travel is related to the solenoid stroke and the valve lash. Accordingly, the actuator assembly  4200  can selectively vary the valve travel by adjusting the solenoid stroke. Moreover, because the housing  4240  is fixedly coupled to the cylinder head  4132 , the position of the push rod  4212  relative to the valve  4160  when the solenoid  4242  is de-energized remains substantially constant when the actuator assembly  4200  is moved from the first configuration to the second configuration. Similarly stated, the valve lash L remains substantially constant when the actuator assembly  4200  is moved from the first configuration to the second configuration. 
     As shown in  FIGS. 44 and 45 , the variable travel actuator  4250  is coupled to the solenoid coil  4242  via a connector  4251 . In this manner, movement and/or force produced by the variable travel actuator  4250  can result in movement of the solenoid  4242  within the housing  4240 . More particularly, when the variable travel actuator  4250  rotates as shown by the arrow GG in  FIG. 45 , the solenoid coil  4242  moves within the housing  4240  as shown by the arrow HH in  FIG. 45 . The connector  4251  can be any suitable connector, such as, for example, a rod, a cable, a belt or the like. Moreover, the variable travel actuator  4250  can include any suitable mechanism for moving the solenoid coil  4242  within the housing  4240 , such as, for example, a stepper motor, an electronic actuator, a hydraulic actuator, a pneumatic actuator and/or the like. 
       FIGS. 46 and 47  are perspective views of an engine  5100  having a variable travel intake valve actuator assembly  5200  and a variable travel exhaust valve actuator assembly  5300 , according to an embodiment. The engine  5100  includes an engine block  5102 , a cylinder head assembly  5130 , an intake valve actuator assembly  5200  and an exhaust valve actuator assembly  5300 . The engine block  5102  defines a cylinder  5103  (shown in dashed lines in  FIGS. 51, 52, 59 and 60 ) within which a piston (not shown) can be disposed. The cylinder head assembly  5130  is coupled to the engine block  5102  such that a portion of the cylinder head assembly  5130  covers the upper portion of the cylinder  5103  to form a combustion chamber. A gas manifold  5110  is coupled to an upper surface of the cylinder head assembly  5130 . The gas manifold  5110  defines an exhaust gas pathway  5112  and an intake air pathway  5111 . In use, exhaust gas can be conveyed from the cylinder  5103  and into the exhaust gas pathway  5112  via the cylinder head assembly  5130 . Similarly, intake air (and/or any suitable intake charge) can be conveyed from the intake air pathway  5111  into the cylinder  5103  via the cylinder head assembly  5130 . 
     The cylinder head assembly  5130  includes a cylinder head  5132 , an intake valve  5160 I and an exhaust valve  5160 E. Referring to  FIGS. 51-53 , the cylinder head  5132  defines an intake valve pocket  5138 I within which the intake valve  5160 I is movably disposed. The cylinder head  5132  defines a set of cylinder flow passages  5148 I and a set of intake manifold flow passages  5144 I. Each of the cylinder flow passages  5148 I is in fluid communication with the cylinder  5103  (shown in dashed lines) and the intake valve pocket  5138 I. Similarly, each of the intake manifold flow passages  5144 I is in fluid communication with the intake air pathway  5111  of the gas manifold  5110  and the intake valve pocket  5138 I of the cylinder head  5132 . As described in more detail herein, in this arrangement, when the intake valve  5160 I is in the closed position (e.g.,  FIG. 51 ), the intake pathway  5111  of the gas manifold  5110  is fluidically isolated from the cylinder  5103 . Conversely, when the intake valve  5160 I is in an opened position (e.g.,  FIGS. 52 and 53 ), the intake pathway  5111  of the gas manifold  5110  is in fluid communication with the cylinder  5103 . Accordingly, the timing and/or amount of intake air conveyed into the cylinder  5103  can be controlled by varying the opening and closing events of the intake valve  5160 I. Although the intake valve  5160 I is shown as having two opened positions ( FIGS. 52 and 53 ), as described in more detail below, the intake valve actuator assembly  5200  can selectively vary the distance through which the intake valve  5160 I travels when moved between the closed position and the opened position. In this manner, the intake valve  5160 I can be moved between the closed position and any number of different partially opened positions. 
     Referring to  FIGS. 59-61 , the cylinder head  5132  defines an exhaust valve pocket  5138 E within which the exhaust valve  5160 E is movably disposed. The cylinder head  5132  defines a set of cylinder flow passages  5148 E and a set of exhaust manifold flow passages  5144 E. Each of the cylinder flow passages  5148 E is in fluid communication with the cylinder  5103  (shown in dashed lines) and the exhaust valve pocket  5138 E. Similarly, each of the exhaust manifold flow passages  5144 E is in fluid communication with the exhaust pathway  5112  of the gas manifold  5110  and the exhaust valve pocket  5138 E of the cylinder head  5132 . As described in more detail herein, in this arrangement, when the exhaust valve  5160 E is in the closed position (e.g.,  FIG. 59 ), the exhaust pathway  5112  of the gas manifold  5110  is fluidically isolated from the cylinder  5103 . Conversely, when the exhaust valve  5160 E is in an opened position (e.g.,  FIGS. 60-61 ), the exhaust pathway  5112  of the gas manifold  5110  is in fluid communication with the cylinder  5103 . Accordingly, timing and/or amount of exhaust gas conveyed out of the cylinder  5103  can be controlled by varying the opening and closing events of the exhaust valve  5160 E. Although the exhaust valve  5160 E is shown as having only two opened positions ( FIGS. 60 and 61 ), as described in more detail below, the exhaust valve actuator assembly  5300  can selectively vary the distance through which the exhaust valve  5160 E travels when moved between the closed position and the opened position. In this manner, the exhaust valve  5160 E can be moved between the closed position and any number of different partially opened positions. 
     Referring to  FIGS. 54-56 , the intake valve  5160 I has tapered portion  5162 I, a first end portion  5176 I and a second end portion  5177 I, and defines a center line CL I . As shown in  FIG. 55 , the second end portion  5177 I defines a threaded opening  5178 I within which the intake pull rod  5212  is threadedly coupled. The second end portion  5177 I includes a spring engagement surface  5179  against which the intake valve spring  5118 I is disposed (see e.g.,  FIGS. 51-53 ). In this manner, the intake valve  5160 I can be biased in the closed position within the intake valve pocket  5138 I. 
     The tapered portion  5162 I of the intake valve  5160 I includes a first surface  5164 I and a second surface  5165 I. As shown in  FIG. 56 , the first surface  5164 I and the second surface  5165 I are each curved surfaces having a radius of curvature R I  about an axis parallel to the center line CL I . Although the first surface  5164 I and the second surface  5165 I are shown has having the same radius of curvature, in other embodiments, the radius of curvature of the first surface  5164 I can be different from the radius of curvature of the second surface  5165 I. Similarly stated in some embodiments, the tapered portion  5162 I of the intake valve  5160 I can be asymmetrical when viewed in a plane substantially normal to the center line CL I . The radius of curvature R I  can have any suitable value. In some embodiments, the radius of curvature R I  can be approximately 114 mm (4.5 inches). 
     As shown in  FIG. 54 , which illustrates a top view of the intake valve  5160 I, the tapered portion  5162 I of the intake valve  5160 I has a first taper angle Θ I . Similarly stated, a width of the tapered portion  5162 I as measured along a first axis normal to the center line CL I  linearly decreases along the center line CL I . As shown in  FIG. 55 , which presents a side view of the intake valve  5160 I, the first surface  5164 I and the second surface  5165 I are angularly offset from each other by a second taper angle α I . Similarly stated, a thickness of the tapered portion  5162 I as measured along a second axis normal to the center line CL I  linearly decreases along the center line CL I . In this manner, the tapered portion  5162 I of the intake valve  5160 I is tapered in two dimensions. The first taper angle Θ I  and the second taper angle α I  can have any suitable value. For example, in some embodiments, the first taper angle Θ I  has a value of between approximately 3 degrees and approximately 10 degrees and the second taper angle α I  has a value of approximately 10 degrees (5 degrees for each side). 
     The tapered portion  5162 I of the intake valve  5160 I defines a set of flow passages  5168 I therethrough (only one flow passage is labeled in  FIGS. 54 and 55 ). As shown in  FIG. 55 , the flow passages  5168 I are angularly offset from the center line CL I  of the intake valve  5160 I by an angle β I  greater than ninety degrees. Similarly stated, a longitudinal axis A FP  of each flow passage  5168 I is non-normal to the center line CL E  In this manner, as shown in  FIGS. 51-53 , when the intake valve  5160 I is disposed within the intake valve pocket  5138 I such that the center line CL I  of the intake valve  5160 I is non-normal to a center line CL cyl  of the cylinder, the longitudinal axis A FP  of each flow passage  5168 I is substantially normal to the center line CL cyl  the cylinder. 
     As shown in  FIG. 54 , each flow passage  5168 I does not have the same shape and/or size as the other flow passages  5168 I. Rather, the size of the flow passages  5168 I closer to the ends of the tapered portion  5162 I is smaller than the size of the flow passages  5168 I at the center of the tapered portion  5162 I. In this manner, the size (e.g., length) of the flow passages  5168 I can correspond to the size and/or shape of the cylinder  5103 . 
     The first surface  5164 I of the tapered portion  5162 I and the second surface  5165 I of the tapered portion  5162 I each include a set of sealing portions (not shown in  FIGS. 54-56 ) that correspond to the flow passages  5168 I. As described above, the sealing portions substantially circumscribe the openings of the first surface  5164 I and the second surface  5165 I. Thus, when the intake valve  5160 I is in the closed position, the sealing portions engage and/or contact the surface of the cylinder head  5132  that defines the intake valve pocket  5138 I such that the cylinder flow passages  5148 I and the intake manifold flow passages  5144 I are fluidically isolated from the intake valve pocket  5138 I. 
     Referring to  FIGS. 62-64 , the exhaust valve  5160 E has tapered portion  5162 E, a first end portion  5176 E and a second end portion  5177 E, and defines a center line CL E . As shown in  FIG. 63 , the second end portion  5177 E defines a threaded opening  5178 E within which the exhaust pull rod  5312  is threadedly coupled. The tapered portion  5162 E of the exhaust valve  5160 E includes a first surface  5164 E and a second surface  5165 E. As shown in  FIG. 64 , the first surface  5164 E and the second surface  5165 E are each curved surfaces having a radius of curvature R E  about an axis parallel to the center line CL E  Although the first surface  5164 E and the second surface  5165 E are shown has having the same radius of curvature, in other embodiments, the radius of curvature of the first surface  5164 E can be different from the radius of curvature of the second surface  5165 E. Similarly stated in some embodiments, the tapered portion  5162 E of the exhaust valve  5160 E can be asymmetrical when viewed in a plane substantially normal to the center line CL I . The radius of curvature R E  can have any suitable value. In some embodiments, the radius of curvature R E  can be approximately can be approximately 47 mm (1.85 inches). 
     As shown in  FIG. 62 , which illustrates a top view of the exhaust valve  5160 E, the tapered portion  5162 E of the exhaust valve  5160 E has a first taper angle Θ E . Similarly stated, a width of the tapered portion  5162 E as measured along a first axis normal to the center line CL E  linearly decreases along the center line CL E . As shown in  FIG. 63 , which presents a side view of the exhaust valve  5160 E, the first surface  5164 E and the second surface  5165 E are angularly offset from each other by a second taper angle α E . Similarly stated, a thickness of the tapered portion  5162 E as measured along a second axis normal to the center line CL E  linearly decreases along the center line CL E . In this manner, the tapered portion  5162 E of the exhaust valve  5160 E is tapered in two dimensions. The first taper angle Θ E  and the second taper angle α E  can have any suitable value. For example, in some embodiments, the first taper angle Θ E  has a value of between approximately 3 degrees and approximately 10 degrees and the second taper angle α E  has a value of approximately 10 degrees (5 degrees for each side). 
     The tapered portion  5162 E of the exhaust valve  5160 E defines a set of flow passages  5168 E therethrough (only one flow passage is labeled in  FIGS. 62 and 63 ). As shown in  FIG. 63 , the flow passages  5168 E are angularly offset from the center line CL E  of the exhaust valve  5160 E by an angle β E  greater than ninety degrees. Similarly stated, a longitudinal axis A FP  of each flow passage  5168 E is non-normal to the center line CL E . In this manner, as shown in  FIGS. 59-61 , when the exhaust valve  5160 E is disposed within the exhaust valve pocket  5138 E such that the center line CL E  of the exhaust valve  5160 E is non-normal to a center line CL cyl  of the cylinder, the longitudinal axis A FP  of each flow passage  5168 E is substantially normal to the center line CL cyl  the cylinder. 
     As shown in  FIG. 62 , each flow passage  5168 E does not have the same shape and/or size as the other flow passages  5168 E. Rather, the size of the flow passages  5168 E closer to the ends of the tapered portion  5162 E is smaller than the size of the flow passages  5168 E at the center of the tapered portion  5162 E. In this manner, the size (e.g., length) of the flow passages  5168 E can correspond to the size and/or shape of the cylinder  5103 . 
     The first surface  5164 E of the tapered portion  5162 E and the second surface  5165 E of the tapered portion  5162 E each include a set of sealing portions (not shown in  FIGS. 62-64 ) that correspond to the flow passages  5168 E. As described above, the sealing portions substantially circumscribe the openings of the first surface  5164 E and the second surface  5165 E. Thus, when the exhaust valve  5160 E is in the closed position, the sealing portions engage and/or contact a surface of the cylinder head  5132  that defines the exhaust valve pocket  5138 E such that the cylinder flow passages  5148 E and the exhaust manifold flow passages  5144 E are fluidically isolated from the exhaust valve pocket  5138 E. 
     Referring to  FIGS. 49 and 51-53 , the intake valve  5160 I is movably disposed within the intake valve pocket  5138 I of the cylinder head  5132 . A plug  5182  is disposed within the intake valve pocket  5138 I adjacent the second end portion  5177 I of the intake valve  5160 I. The plug  5182  has a tapered outer surface that corresponds to the shape of the intake valve pocket  5138 I. In this manner, the outer surface of the plug  5182  and the surface defining the intake valve pocket  5138 I can form a substantially fluid-tight seal. Moreover, the tapered outer surface of the plug  5182  prevents further inward movement of the plug  5182  when the plug  5182  is disposed within the intake valve pocket  5138 I. A spacer  5184  is disposed at least partially within the intake valve pocket  5138 I in contact with the plug  5182 . The spacer  5184  provides a mechanism by which the plug  5182  can be securely coupled within the intake valve pocket  5138 I. The spacer  5184  can be coupled within the valve pocket  5138 I by a set screw, a clamping force exerted by the housing  5270  or the like. 
     As shown in  FIG. 52 , when the intake valve  5160 I is in the fully opened position, the spring engagement surface  5179  of the intake valve  5160 I is spaced apart from the end of the plug  5182 . Thus, the plug  5182  does not provide a positive stop to limit the travel of the intake valve  5160 I within the valve pocket  5138 I. Rather, as described more detail below, the travel of the intake valve  5160 I is controlled by the intake valve actuator assembly  5200 . Moreover, as shown in  FIGS. 51-53 , the sleeve  5182  defines a spring groove  5183  within which an end portion of the intake valve spring  5118 I is disposed. The opposite end portion of the intake valve spring  5118 I is in contact with the spring engagement surface  5179  of the intake valve  5160 I. In this manner, the intake valve  5160 I is biased in the closed position within the intake valve pocket  5138 I. 
     Referring to  FIGS. 49, 59-61 , the exhaust valve  5160 E is movably disposed within the exhaust valve pocket  5138 E of the cylinder head  5132 . A plug  5180  is disposed within the exhaust valve pocket  5138 E adjacent the second end portion  5177 E of the exhaust valve  5160 I. The plug  5180  has a tapered outer surface that corresponds to the shape of the exhaust valve pocket  5138 I. In this manner, the outer surface of the plug  5180  and the surface defining the exhaust valve pocket  5138 E can form a substantially fluid-tight seal. Moreover, when the plug  5180  is disposed within the exhaust valve pocket  5138 I, the tapered arrangement prevents further inward movement of the plug  5182 . A spacer  5181  is disposed at least partially within the exhaust valve pocket  5138 E in contact with the plug  5180 . The spacer  5181  provides a mechanism by which the plug  5180  can be securely coupled within the exhaust valve pocket  5138 I, as described above. 
     As shown in  FIG. 60 , when the exhaust valve  5160 E is in the fully opened position, the shoulder of the exhaust valve  5160 E is spaced apart from the end of the plug  5182 . In this manner, the plug  5182  does not provide a positive stop to limit the travel of the exhaust valve  5160 E within the valve pocket  5138 I. Rather, as described more detail below, the travel of the exhaust valve  5160 E is controlled by the exhaust valve actuator assembly  5300 . In contrast to the intake valve train, as shown in  FIGS. 59-61 , the exhaust valve spring  5118 E is disposed outside of the exhaust valve pocket  5138 E. In this manner, the exhaust valve spring  5118 E is not exposed to the high temperatures associated with the exhaust gas. As discussed in more detail herein, the exhaust valve spring  5118 E is disposed within the exhaust valve actuator assembly  5300 . 
     As described in more detail below, the intake actuator assembly  5200  is configured to move the intake valve  5160 I between its closed position and its opened position and selectively vary the distance through which the intake valve  5160 I travels when moving between its closed position and an opened position. Similarly stated, the intake actuator assembly  5200  is configured to move the intake valve  5160 I between its closed position ( FIG. 51 ) and any number of different opened positions. Referring to  FIG. 50 , the intake actuator assembly  5200  includes a housing  5270  that contains a valve actuator  5210  and a variable travel actuator  5250 . More particularly, the housing  5270  defines a first cavity  5272 , within which the valve actuator  5210  is disposed, and a second cavity  5275 , within which a portion of the variable travel actuator  5250  is disposed. As shown in  FIGS. 46 and 47 , the housing  5270  is coupled to the cylinder head  5132  such that at least a portion of the first cavity  5272  is aligned with the intake valve pocket  5138 I. In this manner, as described in more detail below, the valve actuator  5210  can engage and/or actuate the intake valve  5160 I. Note that  FIGS. 51-53  shows the housing  5270  as being spaced apart from the cylinder head  5132  for purposes of clarity. 
     The valve actuator  5210  is a electronic actuator configured to move the intake valve  5160 I between its closed position and its opened position. The valve actuator  5210  includes a solenoid assembly  5230 , a pull rod  5212  and an armature  5222 . The solenoid assembly  5230  includes a solenoid casing  5240 , a solenoid coil  5242  and an end stop  5231 . The solenoid casing  5240  has a threaded portion  5246  corresponding to a threaded portion  5273  side wall of the housing  5270  that defines the first cavity  5272 . Similarly stated, the outer surface of the solenoid casing  5240  includes male threads configured to mate with the female threads  5273  within the first cavity  5272  of the housing  5270 . In this manner, the solenoid assembly  5230  can be threadedly coupled within the first cavity  5272  of the housing  5270 . Thus, rotation of the solenoid assembly  5230  relative to the housing  5270  results in axial movement of the solenoid assembly  5230  within the first cavity  5272 , as shown by the arrow II in  FIG. 53 . In this manner, as described in more detail below, the solenoid stroke (i.e., the distance between the solenoid assembly  5230  and the armature  5222  when the solenoid is not energized) can be selectively adjusted. 
     The solenoid coil  5242  is disposed within the solenoid casing  5240  such that the lead wire  5241  of the solenoid coil  5242  are accessible from a region outside of the solenoid casing  5240 . Moreover, the solenoid coil  5242  is fixedly disposed within the solenoid casing  5240 . Similarly stated, the solenoid coil  5242  is disposed within the housing  5240  such that movement of the solenoid coil  5242  relative to the housing  5240  is prevented. 
     The end stop  5231  has a flanged portion  5237  and an end surface  5235 . The flanged portion  5237  is coupled to the solenoid casing  5240  such that the solenoid coil  5242  is enclosed and/or contained within the solenoid casing  5240 . The flanged portion  5237  can be coupled to the solenoid casing  5240  in any suitable manner, such as, for example, using cap screws, a snap ring, a welded joint, an adhesive and/or the like. When the end stop  5231  is coupled to the solenoid casing  5240 , the end surface  5235  is disposed within the central opening of the solenoid coil  5242  (see e.g.,  FIGS. 51-53 ). The end surface  5235  of the end stop  5231  defines a groove  5236  within which an end portion of the armature spring  5232  is disposed. As described in more detail below, the end surface  5235  contacts the armature  5222  when the solenoid assembly  5230  is energized. 
     Referring to  FIG. 57 , the armature  5222  defines a lumen  5225  therethrough, and includes a flange  5221  and a contact surface  5228 . The lumen  5225  is counter-bored such that an inner surface of the armature  5222  has a shoulder  5226 . As described in more detail below, the shoulder  5226  is configured to engage the head  5218  of the pull rod  5212  to limit the axial movement of the armature  5222  relative to the pull rod  5212 . The flange  5221  has a diameter smaller than a diameter of the inner surface  5274  of the first cavity  5272  of the housing  5270  (see e.g.,  FIG. 50 ). In this manner, the armature  5222  can move within the first cavity  5272  of the housing  5270  when the solenoid assembly  5240  is energized and/or de-energized. The contact surface  5228  of the armature  5222  defines a groove  5227  within which an end portion of the armature spring  5232  is disposed. 
     The pull rod  5212  has a first end portion  5213  and a second end portion  5214 . The second end portion  5214  of the pull rod  5212  is coupled to the armature  5222 . More particularly, as shown in  FIG. 57 , the second end portion  5214  of the pull rod  5212  has a head  5218  and defines a retaining ring groove  5219  within which a retaining ring  5220  is disposed. The second end portion  5214  of the pull rod  5212  is disposed within the lumen  5225  of the armature  5222  such that the head  5218  of the pull rod  5212  can engage and/or contact the shoulder  5226  of the armature  5222  to limit axial movement of the armature  5222  relative to the pull rod  5212  in a direction shown by the arrow JJ in  FIG. 57 . 
     When the second end portion  5214  of the pull rod  5212  is coupled to the armature  5222 , the retaining ring  5220  is configured to contact the flange  5221  of the armature  5222  to limit axial movement of the armature  5222  relative to the pull rod  5212  in a direction shown by the arrow KK in  FIG. 57 . As shown in  FIG. 57 , the distance d 1  between the head  5218  and the snap ring  5220  is greater than the distance d 2  between the shoulder  5226  of the armature  5222  and the flange  5221  of the armature. In this manner, when the second end portion  5214  of the pull rod  5212  is coupled to the armature  5222 , the armature  5222  can move axially relative to the pull rod  5212  by a predetermined amount (i.e., the difference between d 1  and d 2 ). Moreover, as described above, a first end of the armature spring  5232  is disposed within the groove  5236  of the end stop  5231  and a second end of the armature spring  5232  is disposed within the groove  5227  of the armature  5222 . Thus, when the solenoid assembly  5230  is not energized, the armature  5222  is biased in a position such that the flange  5221  is in contact with the snap ring  5220 . Accordingly, when the solenoid assembly  5230  is energized, the armature  5222  initially travels relative to the pull rod  5212  in the direction shown by the arrow JJ in  FIG. 57 . When the shoulder  5226  of the armature  5222  contacts the head  5218  of the pull rod  5212 , the armature  5222  and the pull rod  5212  move together until the contact surface  5228  of the armature engages and/or contacts the end surface  5235  of the end stop  5231 . By allowing the armature  5222  to move relative to the pull rod  5212  when the solenoid assembly  5230  is energized, the armature  5222  can accelerate and thereby generate an impulse force before engaging the pull rod  5212 . This arrangement can provide more repeatable and/or reliable valve opening performance. 
     The distance through which the armature  5222  can move axially relative to the pull rod  5212  (i.e., the difference between d 1  and d 2 ) can be any suitable amount. In some embodiments, for example, the difference between the spacing of the head  5218  and the groove  5219  (d 1 ) and the thickness of the armature  5222  (d 2 ) is between 0.015 inches and 0.050 inches. In other embodiments, the difference between d 1  and d 2  is approximately 0.030 inches. 
     As described above, the first end portion  5213  of the pull rod  5212  is coupled to second end portion  5177 I of the intake valve  5160 I. More particularly, the first end portion  5213  of the pull rod  5212  includes a male threaded portion disposed within the female threaded opening  5178 I of the intake valve  5160 I. Accordingly, axial movement of the pull rod  5212  results in axial movement of the intake valve  5160 I. In some embodiments, a lock nut can be disposed about the first end portion  5213  of the pull rod  5212  to limit rotational movement of the pull rod  5212  relative to the intake valve  5160 I (i.e., to prevent the pull rod  5212  from “backing out” of the threaded opening  5178 I of the intake valve  5160 I). 
     In use, when the solenoid coil  5242  is energized with an electrical current, a magnetic field is produced that exerts a force upon the armature  5222  in a direction shown by the arrow LL in  FIG. 52 . The magnetic force causes the armature  5222  to move relative to (and towards) the solenoid coil  5242 , as shown by the arrow LL in  FIG. 52  and the arrow JJ in  FIG. 57 . As described above, the armature  5222  initially travels relative to the pull rod  5212 . When the shoulder  5226  of the armature  5222  contacts the head  5218  of the pull rod  5212 , and the force exerted by the pull rod  5212  on the intake valve  5160 I is greater than the biasing force exerted by the spring  5118 I, the armature  5222  and the pull rod  5212  move together, thereby causing the intake valve  5160 I to move from the closed position ( FIG. 51 ) to the opened position ( FIG. 52 ). The armature  5222  and pull rod  5212  travel together until the contact surface  5228  of the armature  5222  engages and/or contacts the end surface  5235  of the end stop  5231 . When the solenoid coil  5242  is energized, the armature  5222  travels through a distance Sd (i.e., the solenoid stroke as shown in  FIG. 51 ). The distance through which the pull rod  5212  (and therefore the intake valve  5160 I) travels is the difference between the solenoid stroke and the difference between d 1  and d 2 , as given by equation (6).
 
Travel= Sd −( d 1− d 2)  (6)
 
Thus, the travel of the intake valve  5160 I can be adjusted by changing the solenoid stroke Sd.
 
     When the solenoid coil  5242  is de-energized, the force exerted by the intake valve spring  5118 I causes the intake valve  5160 I, the pull rod  5212  and armature  5222  to travel in a direction opposite the direction shown by the arrow LL in  FIG. 52 . Additionally, the force exerted by the armature spring  5232  moves the armature  5222  relative to the pull rod  5212  such that the flange  5221  of the armature  5222  is in contact with the snap ring  5220 . 
     The variable travel actuator  5250  is configured to selectively vary the distance through which the intake valve  5160 I travels when moving between the closed and an opened position. More particularly, the variable travel actuator  5250  is configured to selectively adjust the stroke of the solenoid assembly  5230 . In this manner, the intake valve  5160 I can be moved between the closed position and any number of different partially opened positions. Moreover, because the valve actuator  5210  is electrically operated, the valve  5160  can be moved between the closed position and an opened position independently from the rotational position of a camshaft or a crankshaft of the engine  5100 . 
     As shown in  FIG. 50 , the variable travel actuator  5250  includes a motor  5262 , a drive belt  5260  and a driven ring  5252 . As described herein, the variable travel actuator  5250  is configured to selectively rotate the solenoid assembly  5230  within the housing  5270  to adjust the solenoid stroke Sd (see e.g.,  FIG. 51 ). The motor  5262  includes a drive shaft  5263  and a drive member  5265 . The motor  5262  can be, for example a stepper motor, such as the Model 23Y104S-LWB 2A/phase series stepper motor available from Anaheim Automation, Inc. The motor  5262  is coupled to the housing  5270  via a motor housing  5264 . The motor housing  5264  aligns the motor  6262  relative to the housing  5270  such that the drive member  5265  is disposed within the second cavity  5275  of the housing  5270 . 
     The driven ring  5252  includes an outer surface  5254  having a series of protrusions (e.g., teeth or knurling). The driven ring  5252  is coupled to the end stop  5231  of the solenoid assembly  5230  such that rotation of the driven ring  5252  results in rotation of the solenoid assembly  5230 . The driven ring  5252  can be coupled to the end stop  5231  in any suitable manner. For example, in some embodiments, the driven ring  5252  can be coupled to the end stop  5231  via cap screws, a welded joint, an adhesive, a snap-ring and/or the like. The drive belt  5260  is disposed about the drive member  5265  and the outer surface  5254  of the driven ring  5252 . In this manner, rotational movement of the drive shaft  5263  can be transferred to the solenoid assembly  5230  via the drive belt  5260 . 
     A position ring  5257  is coupled to the driven ring  5252  such that the position ring rotates with the driven ring  5252 . The position ring  5257  includes a protrusion  5258  (see e.g.,  FIG. 58 ) configured to engage the sensor  5266 . In this manner, the rotational position of the solenoid assembly  5230  can be measured electronically. Although the sensor  5266  is shown as sensing the rotational position of the solenoid assembly  5230  via contact with the protrusion  5258 , in other embodiments, the sensor  5266  can use any suitable mechanism for sensing the position of the solenoid assembly  5230 . For example, in some embodiments, the sensor  5266  can include an optical shaft encoder configured to provide an electronic output associated with the rotational position of the solenoid assembly  5230 . 
     The variable travel actuator  5250  is configured to selectively vary the valve travel by moving the intake valve actuator assembly  5200  between any number of different configurations corresponding to the position of the solenoid assembly  5130  within the housing  5270 . For example,  FIGS. 51 and 52  show the intake valve actuator assembly  5200  in a first (or full opening) configuration, and  FIG. 53  shows the intake valve actuator assembly  5200  in a second (or partial opening) configuration. When the intake valve actuator assembly  5200  is in the full opening configuration, end surface  5235  of the end stop  5231  is spaced apart from a shoulder of the housing  5270  by a distance d 3 . The shoulder is identified only as a reference point for purposes of showing the position of the solenoid assembly  5230  within the housing  5270 . Thus, when the intake valve actuator assembly  5200  is in the full opening configuration, the solenoid stroke Sd is at its maximum value. Accordingly, when the solenoid assembly  5230  is energized, the intake valve  5160 I moves from the closed position ( FIG. 51 ) to the fully opened position ( FIG. 52 ). When the intake valve  5160 I is in the fully opened position, each flow opening  5168 I of the intake valve  5160 I is substantially aligned with the corresponding intake manifold flow passages  5144 I and cylinder flow passages  5148 I. 
     To move the intake valve actuator assembly  5200  to another configuration (e.g., the partial opening configuration, as shown in  FIG. 53 ), the motor  5262  is energized thereby causing rotational motion of the drive shaft  5263 . The rotational movement of the drive shaft  5263  is transmitted to the driven ring  5252  via the belt  5260 , thereby causing the solenoid assembly  5230  to rotate within the housing  5270 , as shown by the arrow MM in  FIG. 53 . Because the solenoid assembly  5230  is threadedly coupled to the housing  5270 , the rotation of the solenoid assembly  5230  results in axial movement of the solenoid assembly  5230  within the housing  5270 , as shown by the arrow NN in  FIG. 53 . 
     When the intake valve actuator assembly  5200  is in the partial opening configuration, end surface  5235  of the end stop  5231  is spaced apart from a shoulder of the housing  5270  by a distance d 4  that is less than the distance d 3 . Thus, when the intake valve actuator assembly  5200  is in the partial opening configuration, the solenoid stroke (not shown in  FIG. 53 ) less than the maximum value Sd. Accordingly, when the solenoid assembly  5230  is energized, the intake valve  5160 I moves from the closed position ( FIG. 51 ) to the partially opened position ( FIG. 53 ). When the intake valve  5160 I is in the partially opened position, each flow opening  5168 I of the intake valve  5160 I is partially aligned with the corresponding intake manifold flow passages  5144 I and cylinder flow passages  5148 I. Thus, when the intake valve  5160 I is in the partially opened position, the intake air flow rate through the cylinder head assembly  5130  is less than the air flow rate through the cylinder head assembly  5130  when the intake valve  5160 I is in the fully opened position. 
     In a similar manner as described above with reference to the intake actuator assembly  5200 , the exhaust actuator assembly  5300  is configured to move the exhaust valve  5160 E between its closed position and its opened position and selectively vary the distance through which the exhaust valve  5160 E travels when moving between its closed position and an opened position. Similarly stated, the exhaust actuator assembly  5300  is configured to move the exhaust valve  5160 E between its closed position ( FIG. 59 ) and any number of different opened positions (e.g.,  FIGS. 60 and 61 ). Referring to  FIG. 58 , the exhaust actuator assembly  5300  includes a housing  5370  that contains a valve actuator  5210  and a variable travel actuator  5250 . 
     The housing  5370  defines a first cavity  5372 , a second cavity  5375  and a third cavity  5376 . The first cavity  5372  is defined by a side wall that includes a female threaded portion  5373  that corresponds to the male threads  5246  on the solenoid casing  5240 . In this manner, a portion of the valve actuator  5210  is movably disposed within the first cavity  5372 . As described above with reference to the intake actuator assembly  5200 , a portion the variable lift actuator  5250  is disposed within the second cavity  5375 . 
     As shown in  FIGS. 58-61 , the third cavity  5376  contains the exhaust valve spring  5118 E. The side wall that defines the third cavity  5376  includes a spring shoulder  5377  against which a first end of the exhaust valve spring  5118 E is disposed. A second end of the exhaust valve spring  5118 E is disposed within a groove  5317  of a lock nut  5316  coupled to the first end  5213  of the pull rod  5212 . In this manner, the exhaust valve  5160 E is biased in the closed position within the exhaust valve pocket  5138 E. By disposing the exhaust valve spring  5118 E outside of the exhaust valve pocket  5138 E, the exhaust valve spring  5118 E is not directly exposed to hot exhaust gases. Additionally, the side wall adjacent the third cavity  5376  defines a coolant passage  5378  within which coolant can flow to further maintain the exhaust valve spring  5118 E and associated components below a desired temperature. 
     As shown in  FIGS. 46 and 47 , the housing  5370  is coupled to the cylinder head  5132  such that at least a portion of the first cavity  5372  and the third cavity  5376  are aligned with the exhaust valve pocket  5138 E. In this manner, as described above, the valve actuator  5210  can engage and/or actuate the exhaust valve  5160 E. As shown in  FIG. 58 , the housing  5370  is coupled to the cylinder head  5132  via a cooling plate  5380 . The cooling plate  5380  includes a set of cooling passages  5382  (only one is identified in  FIG. 58 ), at least one of which is in fluid communication with the coolant passage  5378  of the housing  5370 . In this manner, the cooling plate  5380  can further promote the transfer of heat away from the exhaust valve spring  5118 E, the valve actuator assembly  5210  and/or components of the exhaust valve train. Note that  FIGS. 59-61  show the housing  5270  and the cooling plate  5380  as being spaced apart from the cylinder head  5132  for purposes of clarity. 
     The valve actuator  5210  of the exhaust valve actuator assembly  5300  is the same as the valve actuator  5210  disposed within the intake valve actuator assembly  5200  as shown and described above. Similarly, the variable travel actuator  5250  of the exhaust valve actuator assembly  5300  is the same as the variable travel actuator  5250  disposed within the intake valve actuator assembly  5200  as shown and described above. Accordingly, the components within and the operation of the valve actuator  5210  and the variable travel actuator  5250  are not described below. In other embodiments, the exhaust valve actuator assembly  5300  can include a valve actuator and/or a variable travel actuator different from the valve actuator  5210  and/or the variable travel actuator  5250 , respectively. For example, in some embodiments, the solenoid assembly of the exhaust valve actuator can produce a different opening force than the solenoid assembly  5230 . 
     The only substantial difference between the exhaust valve actuator assembly  5300  and the intake valve actuator assembly  5200  is that, as described above, the exhaust valve spring  5118 E is disposed within the housing  5370  rather than within the exhaust valve pocket  5138 E. More particularly, as shown in  FIGS. 59-61 , the lock nut  5316  is disposed about the first end portion  5213  of the pull rod  5212 . In some embodiments, the lock nut  5216  can limit rotational movement of the pull rod  5212  relative to the exhaust valve  5160 E (i.e., to prevent the pull rod  5212  from “backing out” of the threaded opening  5178 E of the exhaust valve  5160 E). The lock nut  5316  includes a spring grove  5317  within which an end portion of the exhaust valve spring  5118 E is disposed. In this manner, as described above, the exhaust valve  5160 E is biased in the closed position (see e.g.,  FIG. 59 ). 
     The variable travel actuator  5250  is configured to selectively vary the exhaust valve travel by moving the exhaust valve actuator assembly  5300  between any number of different configurations corresponding to the position of the solenoid assembly  5130  within the housing  5370 . For example,  FIGS. 59 and 60  show the exhaust valve actuator assembly  5300  in a first (or full opening) configuration, and  FIG. 61  shows the exhaust valve actuator assembly  5300  in a second (or partial opening) configuration. When the exhaust valve actuator assembly  5300  is in the full opening configuration, end surface  5235  of the end stop  5231  is spaced apart from a shoulder of the housing  5370  by a distance d 5 . The shoulder is identified only as a reference point for purposes of showing the position of the solenoid assembly  5230  within the housing  5370 . Thus, when the exhaust valve actuator assembly  5300  is in the full opening configuration, the solenoid stroke Sd is at its maximum value. Accordingly, when the solenoid assembly  5230  is energized, the exhaust valve  5160 E moves from the closed position ( FIG. 59 ) to the fully opened position ( FIG. 60 ). When the exhaust valve  5160 E is in the fully opened position, each flow opening  5168 E of the exhaust valve  5160 E is substantially aligned with the corresponding exhaust manifold flow passages  5144 E and cylinder flow passages  5148 E. 
     When the exhaust valve actuator assembly  5300  is in the partial opening configuration, end surface  5235  of the end stop  5231  is spaced apart from a shoulder of the housing  5370  by a distance d 6  that is less than the distance d 5 . Thus, when the exhaust valve actuator assembly  5300  is in the partial opening configuration, the solenoid stroke (not shown in  FIG. 61 ) less than the maximum value Sd. Accordingly, when the solenoid assembly  5230  is energized, the exhaust valve  5160 E moves from the closed position ( FIG. 59 ) to the partially opened position ( FIG. 61 ). When the exhaust valve  5160 E is in the partially opened position, each flow opening  5168 E of the exhaust valve  5160 E is partially aligned with the corresponding exhaust manifold flow passages  5144 E and cylinder flow passages  5148 E. Thus, when the exhaust valve  5160 E is in the partially opened position, the exhaust gas flow rate through the cylinder head assembly  5130  is less than the exhaust gas flow rate through the cylinder head assembly  5130  when the exhaust valve  5160 E is in the fully opened position. 
     Although the intake valve actuator assembly  5200  and the exhaust valve actuator assembly  5300  are shown as having only one partial opening configuration (e.g.,  FIGS. 53 and 61 , respectively), the intake valve actuator assembly  5200  and the exhaust valve actuator assembly  5300  can be moved between the full opening configuration and any number of partial opening configurations. For example in some embodiments, the intake valve actuator assembly  5200  and/or the exhaust valve actuator assembly  5300  can adjust the distance between the closed position and the opened position of the intake valve  5160 I and/or the exhaust valve  5160 E, respectively, to any value between approximately zero inches and 0.090 inches. By selectively varying the distance between the opened position and the closed position (e.g., the valve travel), the intake valve actuator assembly  5200  and/or the exhaust valve actuator assembly  5300  can accurately and/or precisely control the amount and/or flow rate of gas flow into and/or out of the cylinder  5103 . More particularly, the intake valve and/or exhaust valve travel can be varied in conjunction with the timing and duration of the respective valve opening event to provide the desired gas flow characteristics as a function of the engine operating conditions (e.g., low idle, road cruising conditions or the like). Moreover, because the intake valve  5160 I and the exhaust valve  5160 E are not disposed within the cylinder  5103  when the intake valve  5160 I and the exhaust valve  5160 E are in their respective partially opened and/or fully opened positions, the timing of the valve opening can be adjusted without concern for the possibility of valve-to-piston contact. In some embodiments, the control afforded by this arrangement allows the engine gas exchange process to be controlled using only the intake valve  5160 I and the exhaust valve  5160 E, thereby removing the need for a throttle valve upstream of the cylinder head  5132 . 
     This arrangement allows the valve events and/or engine throttling to be tailored for a particular engine operating condition, as well as for a particular engine performance rating or “package.” For example, in certain situations, a particular base engine design (e.g., a 2.2 liter, V6) is used in many different markets (e.g., Europe, California, other U.S. states, high altitude markets and the like), each having different performance and/or emissions requirements. To accommodate the different markets, manufacturers may change the rating or performance “package” of the base engine by changing certain hardware (e.g., the camshafts, the pistons, the fuel injection system or the like). In some embodiments, the valve systems and methods of control described herein can be used to provide multiple different engine ratings or performance “packages” without requiring that engine hardware be changed. 
     For example,  FIG. 65  is a schematic illustration of an engine  6100  according to an embodiment. The engine  6100  includes an engine block  6102  defining at least one cylinder (not identified in  FIG. 65 ). A cylinder head assembly  6130  is coupled to the engine block  6102 . The cylinder head assembly  6130  can be any of the cylinder head assemblies shown and described above, and can include, for example, a tapered valve such as the valves  5160 I and  5160 E shown and described above. The engine  6100  includes an intake valve actuator assembly  6200  and an exhaust valve actuator assembly  6300 . The intake valve actuator assembly  6200  is configured to open the intake valve of the engine  6100  at a predetermined time, for a predetermined duration and/or at a predetermined amount of valve travel, as described above. The exhaust valve actuator assembly  6300  is configured to open the exhaust valve of the engine  6100  at a predetermined time, for a predetermined duration and/or at a predetermined amount of valve travel, as described above. 
     The engine  6100  includes an electronic control unit (ECU)  6196  in communication with the intake valve actuator assembly  6200  and the exhaust valve actuator assembly  6300 . The ECU  6196  is processor of the type known in the art configured to receive input from various sensors (e.g., an engine speed sensor, an exhaust oxygen sensor, an intake manifold temperature sensor or the like), determine the desired engine operating conditions and convey signals to various actuators to control the engine accordingly. As described below, the ECU  6196  is configured determine the desired valve events (e.g., the opening time, duration of opening and/or valve travel) and provide an electronic signal to the intake valve actuator assembly  6200  and the exhaust valve actuator assembly  6300  so that the intake and exhaust valves open and close as desired. 
     The ECU  6196  includes a memory component within which a series of calibration tables are stored. The calibration tables can also be referred to as calibration maps and/or data arrays. The calibration tables can include, for example, a table specifying a target fueling level for the engine  6100  as a function of throttle position, a table specifying a target fuel injector timing and duration as a function of engine operating conditions (e.g., speed and fueling level), a table specifying a target ignition timing as a function of engine operating conditions, and/or the like. The memory of the ECU  6196  also includes calibration tables associated with the intake valve and/or the exhaust valve.  FIGS. 66-68  are tabular representations of calibration tables for the intake valve. Although the calibration tables shown in  FIGS. 66-68  are for the intake valve, the memory of the ECU  6196  can include similar tables for the exhaust valve. 
       FIG. 66  is a valve travel calibration table  6410 . The valve travel calibration table  6410  is a “three dimensional table” that includes a first axis  6412  specifying the target engine speed (e.g., in revolutions per minute). The valve travel calibration table  6410  includes a second axis  6414  specifying the target engine fueling level per operating cycle (e.g., in cubic millimeters of fuel per engine cycle). Although the first axis  6412  and the second axis  6414  specify the target speed and fueling level, respectively, in other embodiments, the axes of the valve travel calibration table  6410  can specify any suitable target engine operating parameter (e.g., target power output, ambient temperature, exhaust oxygen level or the like). The body  6416  of the valve travel calibration table  6410  includes the target valve travel setting (in units of percentage of the maximum travel) for each engine speed (from the first axis  6412 ) and each target fueling level (from the second axis  6414 ). In other embodiments, the body  6416  of the calibration table  6410  can specify the target valve travel in units of length of travel (e.g., inches), steady state airflow at a given valve travel, or the like. The data values provided in the valve travel calibration table  6410  are provided for example only and are not intended to limit the data that can be included in the valve travel calibration table  6410 . 
       FIG. 67  is a valve opening calibration table  6420 . The valve opening calibration table  6420  is a “three dimensional table” that includes a first axis  6422  specifying the target engine speed (e.g., in revolutions per minute). The valve opening calibration table  6420  includes a second axis  6424  specifying the target engine fueling level per operating cycle (e.g., in cubic millimeters of fuel per engine cycle). Although the first axis  6422  and the second axis  6424  specify the target speed and fueling level, respectively, in other embodiments, the axes of the valve opening calibration table  6420  can specify any suitable target engine operating parameter (e.g., target power output, ambient temperature, exhaust oxygen level or the like). The body  6426  of the valve opening calibration table  6420  includes the target valve opening timing (in units of the angular position of the crankshaft in degrees) for each engine speed (from the first axis  6422 ) and each target fueling level (from the second axis  6424 ). In other embodiments, the body  6426  of the valve opening calibration table  6420  can specify the target opening timing in units of time (e.g., milliseconds), relative crankshaft position (e.g., after the fuel injector shuts off), or the like. The data values provided in the valve opening calibration table  6420  are provided for example only and are not intended to limit the data that can be included in the valve opening calibration table  6420 . 
       FIG. 68  is a valve duration calibration table  6430 . The valve opening calibration table  6420  is a “three dimensional table” that includes a first axis  6432  specifying the target engine speed (e.g., in revolutions per minute). The valve duration calibration table  6430  includes a second axis  6434  specifying the target engine fueling level per operating cycle (e.g., in cubic millimeters of fuel per engine cycle). Although the first axis  6432  and the second axis  6434  specify the target speed and fueling level, respectively, in other embodiments, the axes of the valve duration calibration table  6430  can specify any suitable target engine operating parameter (e.g., target power output, ambient temperature, exhaust oxygen level or the like). The body  6436  of the valve duration calibration table  6430  includes the target valve closing timing (in units of the angular position of the crankshaft in degrees) for each engine speed (from the first axis  6432 ) and each target fueling level (from the second axis  6434 ). In other embodiments, the body  6436  of the valve duration calibration table  6430  can specify the target valve open duration in units the crank angle period during which the valve is opened, in units of time (e.g., milliseconds), or the like. The data values provided in the valve duration calibration table  6430  are provided for example only and are not intended to limit the data that can be included in the valve duration calibration table  6430 . 
     During operation of the engine  6100 , the ECU  6196  can control the valve events (e.g., the opening time, duration of opening and/or valve travel of the intake and/or exhaust valve) using the calibration tables  6410 ,  6420  and/or  6430 . More particularly, when the engine is operating at a particular set of operating conditions (e.g., engine speed and fueling level), the ECU  6196  can determine the target valve travel by interpolating (or “looking up”) the target valve travel in the valve travel calibration table  6410  based on the target engine speed and the target fueling level. The target engine speed can be, for example, the engine speed as measured by an engine speed sensor. Under certain conditions (e.g., transient conditions), the target engine speed can be a calculated target based on the current measured engine speed and the temporal history of the measured engine speed (e.g., the rate of change of the engine speed). Similarly, the target fueling level can be, for example, the fueling level as measured determined from another calibration table. Under certain conditions (e.g., transient conditions), the target fueling level can be a calculated target based on the current value for the fueling level and the temporal history of the fueling level (e.g., the rate of change of the fueling level). 
     Similarly, the ECU  6196  can determine the target valve opening timing by interpolating (or “looking up”) the target valve opening timing in the valve opening calibration table  6420  based on the target engine speed and the target fueling level. Similarly, the ECU  6196  can determine the target valve open duration by interpolating (or “looking up”) the target valve duration in the valve duration calibration table  6430  based on the target engine speed and the target fueling level. 
     In this manner, the ECU  6296 , the intake valve actuator assembly  6200  and/or the exhaust valve actuator assembly  6300  can collectively control the amount and/or flow rate of gas into and/or out of the cylinder during engine operation. More particularly, the intake valve and/or exhaust valve timing, duration and/or travel can be varied to provide the desired gas flow characteristics as a function of the engine operating conditions (e.g., low idle, road cruising conditions or the like). In some embodiments, the control afforded by this arrangement allows the engine gas exchange process to be controlled using only the intake valve and/or the exhaust valve, thereby removing the need for a throttle valve upstream of the cylinder head. In such embodiments, the “throttle position” as referenced above, does not refer to the position of a throttle valve, but rather refers to a position of an accelerator pedal, which corresponds to a desired fueling level of the engine. 
     In some embodiments, the ECU  6196  can include one or more “cold start” calibration tables that include target valve travel, timing and/or duration values for use during engine start up. In some embodiments, for example, the ECU  6196  can be configured to open the exhaust valve early (e.g., at a crank angle position of less than 140 crank angle degrees after top dead center on the firing stroke) during a start up event. In this manner, the temperature of the exhaust gas exiting the cylinder can be increased, thereby heating up the catalytic converter faster than could be done with standard exhaust valve events. 
     In some embodiments, the ECU  6196  can include one or more altitude calibration tables that include target valve travel, timing and/or duration values for use when the engine is operating at high altitudes. For example, in some embodiments, an altitude calibration table can include a first axis that specifies atmospheric pressure. 
     In some embodiments, the ECU  6196  can include an idle stability algorithm that adjusts the target valve travel, timing and/or duration values for the valves of a cylinder of a multi-cylinder engine independently from the target valve travel, timing and/or duration values for the valves of an adjacent cylinder of the engine. In this manner, an intake valve of a first cylinder can have a different lift, opening timing and/or duration than an intake valve of a second cylinder. Such an arrangement can allow the engine to maintain idle stability at very low speeds. For example, in some embodiments, such an idle stability algorithm can allow the engine to maintain idle stability at engine speeds below 500 revolutions per minute. 
     Although the engine  6100  is illustrated and described as including an ECU  6196 , in some embodiments, an engine  6100  can include software in the form of processor-readable code instructing a processor to perform the functions described herein. In other embodiments, an engine  6100  can include firmware that performs the functions described herein. 
     While various embodiments have been described above, it should be understood that they have been presented by way of example only, and not limitation. Where methods described above indicate certain events occurring in certain order, the ordering of certain events may be modified. Additionally, certain of the events may be performed concurrently in a parallel process when possible, as well as performed sequentially as described above. While the embodiments have been particularly shown and described, it will be understood that various changes in form and details may be made. 
     For example, although the valves  5160 I and  5160 E are shown and described above as having a tapered portion, in other embodiments, the valves  5160 I and/or  5160 E can be substantially non-tapered. Although the valves  5160 I and  5160 E are shown and described above as being disposed outside of the cylinder  5103  when moved between their respective closed and opened positions, in other embodiments, a portion of the intake valve  5160 I and/or a portion of the exhaust valve  5160 E can be disposed within the cylinder  5103  when in the opened (or partially opened) position. 
     Although the engine  5100  is shown and described as including a single cylinder, in some embodiments, an engine can include any number of cylinders in any arrangement. For example, in some embodiments, an engine can include any number of cylinders in an in-line arrangement. In other embodiments, any number of cylinders can be arranged in a vee configuration, an opposed configuration or a radial configuration. 
     Although movement of the drive shaft  5263  is shown as being transferred to the solenoid assembly  5230  via the drive belt  5260 , in other embodiments, the rotational movement of the drive shaft  5263  can be transferred to the solenoid assembly  5230  via any suitable mechanism, such as, for example, hydraulically, via a gear drive, or the like. 
     Although various embodiments have been described as having particular features and/or combinations of components, other embodiments are possible having a combination of any features and/or components from any of embodiments as discussed above. For example, in some embodiments, a variable travel actuator can selectively vary the valve travel by varying both the valve lash, similar to the variable travel actuator  3250 , and the solenoid stroke, similar to the variable travel actuator  4250 .