Patent Publication Number: US-7717075-B2

Title: Cam mechanism having forced-valve-opening/closing cams and cam-profile setting method

Description:
FIELD OF THE INVENTION 
   The present invention relates to improvements in a cam mechanism having forced-valve-opening/closing cams and cam-profile setting method for the valve-opening/closing cams. 
   BACKGROUND OF THE INVENTION 
   Among the internal combustion engines known today are ones provided with a valve operating device of a forced-valve-opening/closing type that forcibly drives air intake and exhaust valves by means of cams directly or via rocker arms. 
   Such a valve operating device of the forced-valve-opening/closing type requires both cams for opening the valves (i.e., valve-opening cams) and cams for closing the valves (i.e., valve-closing cams). In the case where the valves are driven by means of these valve-opening and valve-closing cams directly or via rocker arms, some clearances are provided between the valve-opening and valve-closing cams and the valves in consideration of respective machining or manufacturing accuracy and assembling accuracy, thermal expansion/shrinkage, etc. of the valves, rocker arms, cams and other valve operating component parts. 
   The above-mentioned clearances can be represented by a valve lift amount difference between a valve lift curve that is indicative of relationship between a rotation angle of the valve-opening cam and a valve lift amount, and a valve lift curve that is indicative of relationship between a rotation angle of the valve-closing cam and a valve lift amount, as will be explained below. 
     FIG. 13  is a graph showing operating characteristics of the conventionally-known valve-opening and valve-dosing cams, where the vertical axis represents the valve lift amounts, valve speeds determined by one of the valve lift amounts and valve acceleration determined by the valve speed while the horizontal axis represents the cam rotation angles. The valve lift curve  301  of the valve-opening cam, which is a curve having a middle curve section of a high mountain shape, has an inflexion point  302  at a cam rotation angle θ 1 , inflexion point  303  at a cam rotation angle θ 3  and maximum lift point  304  at a cam rotation angle θ 2 . 
   The valve lift curve  306  of the valve-closing cam is a curve plotted by displacing the above-mentioned valve lift curve  301  upwardly by a clearance CC, and it has two inflexion points  307  and  308  and maximum lift point  309 . 
   The valve speed curve  311 , which is obtained by differentiating one of the above-mentioned valve lift curves  301  and  306 , has a maximum speed point  312  corresponding to the inflexion points  302  and  307  of the valve lift curves  301  and  306 , a zero speed point  313  corresponding to the maximum lift points  304  and  309  of the curves  301  and  306 , and a minimum speed point  314  corresponding to the inflexion points  303  and  308  of the curves  301  and  306 . 
   Although separate valve speed curves are obtained separately in correspondence with the valve lift curves  301  and  306 , only one of the valve speed curves  311  is shown and described here because the valve speed curves corresponding to the valve lift curves  301  and  306  are of the same shape. 
   The above-mentioned maximum speed point  312  is a “jumping point” where the follower (provided directly on the air intake valve or exhaust valve or on the rocker arm) moves or jumps away from (i.e., disengages from) the operating surface (i.e., cam surface) of the valve-opening cam. Further, reference numeral  316  in  FIG. 13  represents a landing point where the follower lands on the cam surface of the valve-closing cam. Furthermore, VU represents a valve speed at the maximum speed point  312 , and ΔVU represents a difference between the valve speed at the maximum speed point (jumping point)  312  (i.e., jumping speed) and a valve speed at the landing point  316  (i.e., landing speed). The landing speed is a speed at which the follower lands on the cam surface of the valve-closing cam; it should be noted here that the landing speed is distinguished from a colliding speed at which the follower collides against the cam surface of the valve-closing cam (the colliding speed corresponds to the above-mentioned speed difference ΔVU). 
   Similarly, the above-mentioned minimum speed point  314  is a “jumping point” where the follower moves or jumps away from the cam surface of the valve-closing cam. Further, reference numeral  318  in  FIG. 13  represents a landing point where the follower lands on the cam surface of the valve-opening cam. Furthermore, VL represents a valve speed at the minimum speed point  314 , and ΔVL represents a difference between the jumping speed at the minimum speed point (jumping point)  314  and a landing speed at the landing point  318 . The landing speed is a speed at which the follower lands on the cam surface of the valve-opening cam; it should be noted here that the landing speed is distinguished from a colliding speed at which the follower collides against the cam surface of the valve-opening cam (the colliding speed corresponds to the above-mentioned speed difference ΔVL). 
   The valve acceleration curve  321 , which is obtained by differentiating the above-mentioned valve speed curve  311 , has a zero acceleration point  322  corresponding to the maximum speed point  312  of the valve speed curve  311 , a minimum acceleration point  323  corresponding to the zero speed point  313  of the valve speed curve  311 , and a zero acceleration point  324  corresponding to the minimum speed point  314  of the valve speed curve  311 . 
   Although separate valve acceleration curves are obtained separately from the valve speed curves obtained in correspondence with the valve lift curves  301  and  306  as noted above, only one of the valve acceleration curves  321  is explained because the two valve acceleration curves are of the same shape. 
   As stated above, the clearance CC is provided between the valve lift curves  301  and  306 . Thus, in the case where the valves are driven by the cams directly, the intake valve and exhaust valve first temporarily move away from the valve-opening cam and valve-closing cam and then collide with the cams, because of the provision of the clearance CC between the cams. In the case where the valves are driven by the cams via the rocker arms, on the other hand, the rocker arms first temporarily move away from the valve-opening cam and valve-dosing cam and then collide with the cams, because of the provision of the clearance CC between the cams. Thus, in both of the cases, unwanted sound noise would be produced by the provision of the clearances between the cams. 
   Particularly, the inflexion point  302  of the valve lift curve  301  is where the operated member (i.e., the air intake valve, exhaust value or rocker arm), slidably contacting the valve-opening cam, moves away from the operating surface of the valve-opening cam, and the inflexion point  308  of the valve lift curve  306  is where the operated member (i.e., the air intake valve, exhaust value or rocker arm), slidably contacting the valve-closing cam, moves away from the operating surface of the valve-closing cam; thus, the valve speeds take maximum absolute values at these inflexion points. Consequently, at these inflexion points, speeds at which the operated members collide with the operating surfaces of the valve-opening and valve-closing cams become great, which would result in increased sound noise. 
   In order to prevent such unwanted sound noise, there have been proposed, for example in Japanese Patent Application Laid-Open Publication No. SHO-60-108513 (hereinafter referred to as “Patent Literature 1”) or No. HEI-6-221119 (hereinafter referred to as “Patent Literature 2”), an improved valve operating device and cam-profile setting method for an internal combustion engine of the forced-valve-opening/closing type, which are characterized in that the clearance between the valve lift curve of the valve-opening cam and the valve lift curve of the valve-closing cam is partly narrowed. 
     FIG. 14  is a graph showing relationship between the valve lift amounts and the cam rotation angle in the valve operating device for an internal combustion engine disclosed in Patent Literature 1. In the figure, reference character A represents a cam curve of the valve-opening cam, B represents a cam curve of the valve-dosing cam defining a predetermined clearance with respect to the cam curve A, and D represents a cam curve of the valve-closing cam obtained by modifying the cam curve B so as to define a modified clearance with respect to the cam curve A. Namely, in the cam curve D, a curvature in a region “K” between a maximum lift point PE of the cam curve B and a jump start point PD, at which a slipper of a rocker arm driven by the valve-closing cam jumps away from the cam surface of the valve-closing cam toward the cam surface of the valve-opening cam, is set such that the clearance between the cam curves A and D is greater than the clearance between the cam curves A and B. 
   More specifically, in the cam curve D, the jump start point PD is located more rearward, in a rotational direction of the cam, than an inflexion point PB of the cam curve B, namely, closer to the maximum lift point PE of the cam curve B, and a point at which the slipper of the rocker arm jumps from the jump start point PD toward the cam curve A is not only located closer to the maximum lift point PE than an inflexion point PA 2  of the cam curve A but also set in a first region “L”, as counted from the inflexion point PB, among four equally-divided regions of a range from the inflexion point PB to the maximum lift point PE of the cam curve B. Further, PA 1  in  FIG. 14  represents a point where the slipper shifts to the cam curve A after jumping away from the cam curve B. Thus, a section where the slipper of the rocker arm shifts from the cam surface of the valve-closing cam (cam curve D) to the cam surface of the valve-opening cam (cam curve A) has a steep incline, so that impact with which the slipper having jumped at the jump start point PD collides against the cam surface of the valve-opening cam (cam curve A) will be reduced considerably. 
     FIG. 15  is a graph showing relationship between the valve lift amounts and valve train&#39;s inertial force and the cam rotation angle in the valve operating device for an internal combustion engine disclosed in Patent Literature 2. In  FIG. 15 , the vertical axis represents the valve lift amounts and valve train&#39;s inertial force, while the horizontal force represents the cam rotation angles. 
   Further, in  FIG. 15 , E represents a valve lift curve of the valve-opening cam, F represents a valve lift curve of the valve-closing cam defining a predetermined clearance with respect to the valve lift curve E, G represents a valve lift curve of the valve-closing cam obtained by modifying part of the valve lift curve F, H represents a curve of the valve train&#39;s inertial force, C represents a difference between base circle diameters of the valve-opening cam and valve-closing cam. 
   Between the valve lift curve E and valve lift curve G, there are formed a clearance C 0  (e.g., C 0 =0.25 mm for the air intake valve or C 0 =0.35 mm for the exhaust valve) in the valve-opening state, clearance C 1  (e.g., C 1  is about 0.05 mm) at a cam rotation angle J where the direction of the valve train&#39;s inertial force changes, and clearance C 2  (=C 1 ) at the time of a maximum valve lift. 
   With the technique shown in  FIG. 14  (i.e., disclosed in Patent Literature 1), the clearance between the cam curves D and A in the above-mentioned region “L”, machining or manufacturing accuracy and assembling accuracy decreases as the cam rotation angle increases. If the clearance is small like this, the machining or manufacturing accuracy and assembling accuracy of the component parts of the valve train, such as the valve-opening and valve-closing cams, rocker arms and air intake and exhaust valves, has to be enhanced, which would unavoidably invite cost increase. 
   With the technique shown in  FIG. 15  (i.e., disclosed in Patent Literature 2), the clearance is minimized as close to zero as possible over the range from the maximum lift point to the point of the cam rotation angle J where the direction of the valve train&#39;s inertial force changes, and thus, the component parts of the valve train, such as the valve-opening and valve-closing cams, rocker arms, air intake and exhaust valves, must be manufactured and assembled with high accuracy as in the case of the technique disclosed in Patent Literature 1, so that high-accuracy clearance management would require increased necessary cost. Further, if the clearance is small, lubricating oil between the valve-opening and valve-closing cams and the rocker arms would have increased viscosity resistance and agitation resistance, which tends to lower the output and fuel efficiency of the internal combustion engine. 
   SUMMARY OF THE INVENTION 
   In view of the foregoing prior art problems, it is an object of the present invention to achieve cost reduction and performance enhancement of an internal combustion engine by setting relatively great clearances between valve-opening and valve-closing cams and air intake and exhaust valves in a predetermined range of cam rotation angles. 
   It is another object of the present invention to minimize unwanted sound noise in a valve operating device of the forced-valve-opening/closing type by lessening collision between air intake and exhaust valves, or followers provided on rocker arms, and valve-opening and valve-closing cams. 
   According to a first aspect of the present invention, there is provided a cam mechanism having improved valve-opening and valve-closing cams for forcibly driving an air intake valve and exhaust valve. Basic valve lift curve of the valve-opening cam, indicative of relationship between cam rotation angles and valve lift amounts of the valve-opening cam is plotted in a graph where the vertical axis represents valve lift amounts of the air intake valve and exhaust valve and the horizontal axis represents cam rotation angles, and a basic valve lift curve of the valve-closing cam, indicative of relationship between cam rotation angles and valve lift amounts of the valve-closing cam is plotted in the graph by offsetting the basic valve lift curve of the valve-opening cam in a valve-lift-amount increasing direction. No-load valve lift correction curves of the valve-opening and valve-closing cams are set by offsetting a no-load curve section of the basic valve lift curve of the valve-opening cam, along which a corresponding one of the followers for actuating an air intake valve and exhaust valve does not slide, away from the basic valve lift curve of the valve-closing cam and by offsetting a no-load curve section of the basic valve lift curve of the valve-closing cam, along which the follower does not slide, away from the basic valve lift curve of the valve-opening cam, or by modifying the offset no-load curve sections into desired shapes. Respective normal valve lift curves of the valve-opening and valve-closing cams are formed by connecting the corresponding no-load valve lift correction curves with remaining sections of the corresponding basic valve lift curves; thus, a greater clearance can be provided between the normal valve lift curves of the valve-opening and valve-closing cams. The cam profiles of the valve-opening and valve-closing cams are set on the basis of such normal valve lift curves. 
   With the increased clearance between given sections of the normal valve lift curves of the valve-opening and valve-closing cams, the present invention can eliminate the need for high-accuracy management of the clearance between these sections of the normal valve lift curves of the valve-opening and valve-closing cams, and thereby eliminate the need for enhancing the manufacturing accuracy and assembling accuracy of various component parts of the valve operating device; as a result, the present invention can achieve significant cost reduction of the internal combustion engine. Further, with the increased clearance, the present invention can reduce viscosity resistance and agitation resistance of lubricating oil between the valve-opening and valve-closing cams and the corresponding follower and thereby enhance the performance, such as the output and fuel efficiency, of the internal combustion engine. 
   Preferably, the basic valve lift curve of the valve-opening cam and the basic valve lift curve of the valve-closing cam each have a middle curve section of a high mountain shape. Two cam rotation angle ranges including mountain base portions of each of the basic valve lift curves of the valve-opening and valve-closing cams are set as first and second ramp sections, and one of two cam rotation angle ranges, including mountain hillside portions of each of the basic valve lift curves, where the follower of the air intake valve or exhaust valve shifts from the valve-opening cam to the valve-closing cam, is set as a first shift section while the other of the two cam rotation angle ranges, where the follower shifts from the valve-closing cam to the valve-opening cam, is set as a second shift section. Another cam rotation angle range including a mountain top portion of each of the basic valve lift curves being is as a great lift section. The normal valve lift curve of the valve-opening cam is formed by connecting together: the no-load valve lift correction curve of the valve-opening cam, formed by offsetting the great lift section of the basic valve lift curve of the valve-opening cam in a valve-lift-amount decreasing direction; the first and second shift sections of the basic valve lift curve of the valve-opening cam; and the first and second ramp sections of the basic valve lift curve of the valve-opening cam; the cam profile of the valve-opening cam is set on the basis of the normal valve lift curve. Similarly, the normal valve lift curve of the valve-closing cam is formed by connecting together: the no-load valve lift correction curve of the valve-closing cam, formed by the first and second ramp sections of the basic valve lift curve of the valve-closing cam being offset in the valve-lift-amount increasing direction; the first and second shift sections of the basic valve lift curve of the valve-closing cam; and the great lift section of the basic valve lift curve of the valve-closing cam; thus, the cam profile of the valve-closing cam is set on the basis of the normal valve lift curve of the valve-closing cam. 
   In the great lift section, the clearance between the normal valve lift curves of the valve-opening and valve-closing cams can be increased by the great lift section of the basic valve lift curve of the valve-opening cam being offset in the valve-lift-amount decreasing direction. In the first and second ramp sections, the clearance between the normal valve lift curves of the valve-opening and valve-dosing cams can be increased by the first and second ramp sections of the basic valve lift curve of the valve-closing cam being offset in the valve-lift-amount increasing direction. Thus, the clearance has to be managed with high accuracy only in the first and second shift sections; namely, the clearance need not be managed with high accuracy in the other sections than the first and second shift sections. Consequently, high machining or manufacturing accuracy and assembling accuracy is required of the various component parts of the valve operating device, which can thereby achieve significant cost reduction of the internal combustion engine. Further, with the increased clearance, the present invention can reduce the viscosity resistance and agitation resistance of the lubricating oil between the valve-opening and valve-closing cams and the corresponding follower and thereby enhance the performance, such as the output and fuel efficiency, of the internal combustion engine. 
   According to a second aspect of the present invention, a valve lift amount difference is provided between a basic valve lift curve of a valve-opening cam indicative of a relationship between the cam rotation angles and valve lift amounts of the valve-opening cam and a basic valve lift curve of a valve-closing cam indicative of relationship between the cam rotation angles and valve lift amounts of the valve-closing cam. There are set, with respect to the basic valve lift curves of the valve-opening and valve-closing cams, ultimate valve lift curves of the valve-opening and valve-closing cams each including, as cam rotation angle ranges, a first shift section where a corresponding one of the followers for actuating the air intake valve and exhaust valve jumps away from the valve-opening cam and lands on the valve-closing cam and a second shift section where the follower jumps away from the valve-closing cam and lands on the valve-opening cam. Basic speed difference is determined which is indicative of a difference between jumping and landing speeds of the follower on a basic valve speed curve determined from the basic valve lift curves of the valve-opening and valve-closing cams, and an ultimate speed difference is determined which is indicative of a difference between jumping and landing speeds of the follower on an ultimate valve speed curve determined from the ultimate valve lift curves of the valve-opening and valve-closing cams. The respective cam profiles of the valve-opening and valve-closing cams are set in such a manner that the ultimate speed difference is smaller than the basic speed difference. 
   The first and second shift sections are provided on each of the ultimate valve lift curves of the valve-opening and valve-closing cams. In the first shift section, the corresponding follower jumps away from the surface of the valve-opening cam and lands on the surface of the valve-closing cam, while, in the second shift section, the corresponding follower jumps away from the surface of the valve-closing cam and lands on the surface of the valve-opening cam. The basic valve speed curve is determined from the basic valve lift curves of the valve-opening and valve-closing cams, and the basic speed difference is determined which is indicative of the difference between the jumping and landing speeds of the follower on the basic valve speed curve. Further, the ultimate valve speed curve is determined from the ultimate valve lift curves of the valve-opening and valve-closing cams, and the cam profiles are set such that the ultimate speed difference between jumping and landing speeds of the follower on the ultimate valve speed curve is smaller than the basic speed difference. Thus, the speed at which the follower collides against the valve-closing or valve-opening cam can be reduced; as a consequence, the colliding impact and hence sound noise can be significantly reduced. Consequently, even if the clearance between the ultimate valve lift curves of the valve-opening and valve-closing cams is formed into a relatively great size, it is possible to reduce the speed at which the follower collides against the valve-opening or vale-closing cam in the first and second shift sections and thereby lessen the colliding compact; as a result, the present invention can suppress production of sound noise while minimizing the cost. 
   Preferably, the cam profiles are set in such a manner that, in the first and second shift sections, the absolute value of the valve speed at a peak of the ultimate valve speed curve is set to be smaller than the absolute value of the valve speed at a peak of the basic valve speed curve, and that the absolute values of the landing speeds on the ultimate valve speed curve in the first and second shift sections are kept at values higher speed-curve positions than the corresponding absolute values of the landing speeds on the basic valve speed curve. The peak of the basic valve speed curve corresponds to an inflexion point of the basic valve lift curve, and this inflexion point is a point where the follower jumps away from the valve-opening or valve-closing cam. Similarly, the peak of the ultimate valve speed curve corresponds to an inflexion point of the ultimate valve lift curve, and this inflexion point is a point where the follower jumps away from the valve-opening or valve-closing cam. 
   With the arrangement that, in the first and second shift sections, the absolute value of the valve speed at the peak of the ultimate valve speed curve is set to be smaller than the absolute value of the valve speed at the peak of the basic valve speed curve, the jumping speed on the ultimate valve speed curve can be limited appropriately. Further, with the arrangement that the absolute values of the landing speeds on the ultimate valve speed curve in the first and second shift sections are kept constant at respective values corresponding to higher speed-curve positions than the corresponding absolute values of the landing speeds on the basic valve speed curve—more specifically, the absolute value of the landing speed on the valve speed curve in the first shift section (positive speed region) is kept at a constant value greater than the corresponding absolute value of the landing speed of the basic valve speed curve while the absolute value of the landing speed on the valve speed curve in the second shift section (negative speed region) is kept at a constant value smaller than the corresponding absolute value of the landing speed of the basic valve speed curve—, the landing speed on the ultimate valve lift curve can be increased, so that the ultimate speed difference between the jumping speed and the landing speed can be reduced. As a result, the colliding speed at which the follower collides the valve-closing or valve-opening cam, and hence the colliding impact, cam can be significantly reduced. 
   According to a third aspect of the present invention, there is provided an improved method for setting cam profiles of valve-opening and valve-closing cams for forcibly driving an air intake valve and exhaust valve, which the comprises: a first step of plotting a basic valve lift curve on the basis of a predetermined lift amount required of the air intake valve or exhaust valve and a valve speed curve from the basic valve lift curve; a second step of determining a basic speed difference between a jumping speed and a landing speed, on the basic speed curve, when a corresponding one of followers for actuating the air intake valve and exhaust valve jump away from the valve-opening cam and land on the valve-closing cam or when the follower jumps away from the valve-closing cam and lands on the valve-opening cam, and plotting an improved valve speed curve such that an improved speed difference between jumping and landing speeds, on the improved valve speed curve, of the follower is smaller than the basic speed difference; a third step of adjusting integrated values of the valve speeds indicated by the improved valve speed curve to integrated values of the valve speeds indicated by the basic valve speed curve while maintaining the improved speed difference, to thereby obtain an ultimate valve speed curve; and a fourth step of plotting an ultimate valve lift curve on the basis of the ultimate valve speed curve. 
   With the second step of plotting the improved valve speed curve such that the improved speed difference is smaller than the basic speed difference, the colliding speed at which the follower collides against the valve-closing or valve-opening cam, and hence the colliding impact, can be significantly reduced. Further, with the third step of adjusting the integrated values of the valve speeds of the improved valve speed curve to the integrated values of the valve speeds of the basic valve speed curve while maintaining the improved speed difference, the shape of the ultimate valve lift curve can be adjusted to agree with or approach the shape of the basic valve lift curve, except in sections including a range where the follower jumps away from the valve-opening cam and lands on the valve-closing cam or where the follower jumps away from the valve-closing cam and lands on the valve-opening cam. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Certain preferred embodiments of the present invention will hereinafter be described in detail, by way of example only, with reference to the accompanying drawings, in which: 
       FIG. 1  is a sectional view showing a valve operating device for an internal combustion engine according to a first embodiment of the present invention; 
       FIG. 2  is a sectional view showing a valve operating device for an internal combustion engine according to a second embodiment of the present invention; 
       FIG. 3  is a graph showing valve lift amounts, valve speed and valve acceleration related to the valve-opening and valve-closing cams of the present invention; 
       FIG. 4  is a diagram explanatory of operation of the valve lift curves of the valve-opening cam and valve-closing cam of the present invention; 
       FIG. 5  is a graph showing other examples of the valve lift amounts, valve speed and valve acceleration related to the valve-opening and valve-closing cams of the present invention; 
       FIG. 6  is a diagram explanatory of operation of the other examples of the valve lift curves of the valve-opening cam and valve-closing cam of the present invention; 
       FIG. 7  is a diagram explanatory of a former half of an operational sequence for setting cam profiles of the valve-opening cam and valve-closing cam of the present invention; 
       FIG. 8  is a diagram explanatory of a latter half of the operational sequence of the process for setting cam profiles of the valve-opening cam and valve-closing cam of the present invention; 
       FIG. 9  is a diagram showing first modifications of the valve lift curves of the valve-opening and valve-closing cams; 
       FIG. 10  is a diagram showing second modifications of the valve lift curves of the valve-opening and valve-closing cams; 
       FIG. 11  is a diagram showing third modifications of the valve lift curves of the valve-opening and valve-closing cams; 
       FIG. 12  is a diagram showing fourth modifications of the valve lift curves of the valve-opening and valve-closing cams; 
       FIG. 13  is a graph showing relationship between a cam rotation angle and valve lift amounts of conventionally-known valve-opening and valve-closing cams; 
       FIG. 14  is a graph showing relationship between a cam rotation angle and valve lift amounts in a conventionally-known valve operating device for an internal combustion engine; and 
       FIG. 15  is a graph showing a relationship between valve lift amounts and valve train&#39;s inertial force and cam rotation angle in a conventionally-known valve operating device for an internal combustion engine. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1  is a sectional view showing a valve operating device for an internal combustion engine according to a first embodiment of the present invention. The internal combustion engine  10  includes a cylinder head  11  that is provided with a valve operating device  15  of a forced-valve-opening/closing type that forcibly drives an air intake valve  12  and exhaust valve  13  to open and close the valves  12  and  13 . 
   The valve operating device  15  includes a cam shaft  18  rotatably mounted on a cylinder head body  17 , a rocker shaft  21  mounted on the cylinder head body  17 , a rocker arm pivotably mounted on the rocker shaft  21  and drivable by the cam shaft  18 , the air intake valve  12  connected via a connection mechanism  23  to an end of the rocker arm  22  for opening and closing an air intake port  24  of the cylinder head body  17 , and the exhaust valve  13  connected to an end of a rocker arm (not shown) for opening and closing an exhaust port  26  of the cylinder head body  17 . Reference numeral  31  represents a combustion chamber communicating with the air intake port  24  and exhaust port  26 , and  32  represents an ignition plug projecting into the combustion chamber  31 . 
   The cam shaft  18  has a disk section  41  formed thereon in such a manner as to intersect the axis of the shaft  18 , and a cam groove section  42  is formed in a surface  41   a  of the disk section  41 . 
   Cam follower  22   a  formed at the distal end of the rocker arm  22  is inserted in the cam groove  42 , and the cam groove section  42  has a valve-opening cam  44  for opening the air intake valve  12  and a valve-closing cam  45  for closing the air intake valve  12 . The valve-opening cam  44  and valve-closing cam  45  slidingly contact the above-mentioned follower  22   a . Reference numerals  47  and  48  represent valve guides. Separate followers  22   a  are provided in corresponding relation to the air intake vale  12  and exhaust valve  13 . 
     FIG. 2  is a sectional view showing a valve operating device for an internal combustion engine according to a second embodiment of the present invention. The internal combustion engine  60  includes a cylinder head  61  provided with a valve operating device  65  of a forced-valve-opening/closing type that forcibly drives an air intake valve  62  to open and close the valve  62 . 
   The valve operating device  65  includes a cam shaft  67  rotatably mounted on a cylinder head body  61   a , rocker shafts  71  and  72  mounted on the cylinder head body  61   a , a valve-opening rocker arm  73  and valve-closing rocker arm  74  pivotably mounted on the rocker shafts  71  and  72  and driveable by the cam shaft  67 , and the air intake valve  62  driveable by the rocker arms  73  and  74  for opening and closing the air intake port  76 . Reference numeral  78  represents a combustion chamber that communicates with the air intake port  76  when the air intake valve  62  is opened. 
   The cam shaft  67  is provided with a valve-opening cam  81  for driving the valve-opening rocker arm  73 , and a valve-closing cam  82  for driving the valve-closing rocker arm  74 . Reference numeral  81   a  represents a valve-opening cam surface slidingly contacting the valve-opening rocker arm  73 , and  82   a  represents a valve-opening cam surface slidingly contacting the valve-closing rocker arm  74 . 
   The valve-opening rocker arm  73  has a cam-side sliding surface  73   a  slidingly contacting the valve-opening cam  81 , and a valve-side sliding surface  73   b  slidingly contacting an end section  62 A of the air intake valve  62 . 
   The valve-closing rocker arm  74  has a cam-side sliding surface  74   a  slidingly contacting the valve-closing cam  82 , and a valve-side sliding surface  74   b  slidingly contacting the end section  62 A of the air intake valve  62 . 
   The end section  62 A of the air intake valve  62  has a valve-opening-side sliding surface  62   a  that slidingly contacts the valve-side sliding surface  73   b  of the valve-opening rocker arm  73 , and a valve-closing-side sliding surface  62   b  that slidingly contacts the valve-side surface  74   b  of the valve-closing rocker arm  74 . 
   In the instant embodiment, the end section  62 A of the air intake valve  62  corresponds in function to the follower  62   a  in the embodiment of  FIG. 1 . 
     FIG. 3  is a graph showing valve lift amounts, valve speed and valve acceleration related to the valve-opening and valve-closing cams of the present invention, for example, in the case where the air intake valve  12  is opened and closed via the valve-opening cam  44  and valve-closing cam  45  shown in  FIG. 1 . In  FIG. 3 , the same elements as in  FIG. 13  are indicated by the same reference characters as used in  FIG. 13  and will not be described in detail to avoid unnecessary duplication. In  FIG. 3 , the vertical axis represents the valve lift amounts, valve speeds determined by one of the valve lift amounts and valve acceleration determined by the valve speed, while the horizontal axis represents the cam rotation angles. 
   Valve lift curve  101  of the valve-opening cam is different from the valve lift curve  301  of  FIG. 13  in that it has modified portions, i.e. slanted linear portions  101 A and  101 B, in cam rotation angle ranges α 1 -α 2  and α 4 -α 5 . These slanted linear portions  101 A and  101 B have, at their opposite ends, inflexion points  103  and  104  and inflexion points  106  and  107 , respectively. 
   Valve lift curve  111  of the valve-closing cam is different from the valve lift curve  306  of  FIG. 13  in that it has modified portions, i.e. slanted linear portions  111 A and  111 B, in the cam rotation angle ranges α 1 -α 2  and α 4 -α 5 . These slanted linear portions  111 A and  111 B have, at their opposite ends, inflexion points  113  and  114  and inflexion points  116  and  117 , respectively. 
   The cam rotation angle range α 1 -α 2  in the valve lift curve  101  and  111  will hereinafter be referred to as “first shift section”, while the cam rotation angle range α 4 -α 5  in the valve lift curves  101  and  111  will hereinafter be referred to as “second shift section”. The above-mentioned slanted linear portions  101 A and  111 A are parallel to each other, and slanted linear portions  101 B and  111 B are parallel to each other. 
   Valve lift amount difference, i.e. clearance CC, between the valve lift curves  101  and  111  is, for example, 0.1 mm, and the same clearance CC is set in the first shift section and second shift section. Namely, in the instant embodiment, the clearance CC between the valve lift curves  101  and  111  in the first and second shift sections is greater than the clearance in the conventionally-known device shown in  FIG. 14  or  15 , so that component parts of the valve operating device may have lower machining or manufacturing and assembling accuracy. In this way, the instant embodiment can not only reduce the necessary cost of the internal combustion engine but also reduce viscosity and agitation resistance when the follower slides over the valve-opening or valve-closing cam surface, so that output loss of the internal combustion engine can be effectively reduced. 
   The above-mentioned cam rotation angle range α 1 -α 2  is a range where the inflexion points  302  and  307  of the valve lift curves  301  and  306  of  FIG. 13  are present, and the above-mentioned cam rotation angle range α 4 -α 5  is a range where the inflexion points  303  and  308  of the valve lift curves  301  and  306  of  FIG. 13  are present. 
   The cam rotation angle range α 1 -α 2  in the valve speed curve  121  obtained by differentiating the valve lift curve  101  or  111  is in the form of a horizontal linear section  121 A, and the cam rotation angle range α 4 -α 5  in the valve speed curve  121  obtained by differentiating the valve lift curve  101  or  111  is in the form of a horizontal linear section  121 B. 
   The horizontal linear section  121 A is where the valve speed is kept at a constant value lower than the peak in the positive-speed region of the valve speed curve  121 , i.e. the peak in the positive-speed regions or maximum speed point  312  of the valve speed curve  311  of  FIG. 13 . 
   The horizontal linear section  121 B is where the valve speed is maintained at a constant absolute value lower than the peak in the negative-speed region of the valve speed curve  121 , i.e. the peak in the negative-speed region or minimum speed point  314  of the valve speed curve  311  of  FIG. 13 . 
   In  FIG. 3 , reference numeral  123  represents a jumping point where the follower (i.e., follower  22   a  of  FIG. 1  or end section  62 A of  FIG. 2 ) moves or jumps away from (i.e., disengages from) the cam surface of the valve-opening cam, and which is located at the point of the cam rotation angle α 1  on the valve speed curve  121 . This jumping point is a peak point where the valve speed takes the greatest value V 1  in the positive-speed region of the valve speed curve  121 . Further, reference numeral  124  represents a landing point where the follower lands on the valve-closing cam surface, and which is located on the horizontal linear section  121 A. These jumping point  123  and landing point  124  will be later explained in greater detail with reference to  FIG. 4 . 
   Difference between a jumping speed of the follower (valve speed) at the jumping point  123  and a landing speed of the follower (valve speed) at the landing point  124  is indicated by ΔV 1 . 
   In the instant embodiment, the valve speed V 1  at the jumping point  123  is set to be lower than a valve speed at the jumping point  312  (see also  FIG. 13 ) and the valve speed at the landing point  124  is set to be higher than a valve speed at the landing point  316  (see also  FIG. 13 ), so that the speed difference ΔV 1  is smaller than the speed difference ΔVU. 
   Similarly, in  FIG. 3 , reference numeral  127  represents a jumping point where the follower moves or jumps away from the cam surface of the valve-closing cam, and which is located at the cam rotation angle α 4  on the valve speed curve  121 . This jumping point is a peak point where the absolute value of the valve speed takes the greatest value V 2  in the negative-speed region of the valve speed curve  121 . Further, reference numeral  128  represents a landing point where the follower lands on the valve-opening cam surface, and which is located on the horizontal linear section  121 B. These jumping point  127  and landing point  128  will be later explained in greater detail with reference to  FIG. 4 . 
   Difference between a jumping speed of the follower at the jumping point  127  and a landing speed of the follower at the landing point  128  is indicated by ΔV 2 . 
   In the instant embodiment, the absolute value of the valve speed V 2  at the jumping point  127  is set to be lower than the absolute value of a valve speed at the jumping point  314  ( FIG. 13 ) and the absolute value of the valve speed at the landing point  128  is set to be higher than the absolute value of a valve speed at the landing point  318  ( FIG. 13 ), so that the speed difference ΔV 2  is set to be smaller than the speed difference ΔVL of  FIG. 13 . 
   The valve acceleration curve  125  obtained by differentiating the valve speed curve  121  has, in the cam rotation angle range α 1 -α 2 , a linear section  125 A where the valve acceleration is kept constant at a zero value in correspondence with the linear section  121 A of the valve speed curve  121 , and has, in the cam rotation angle range α 4 -α 5 , a linear section  125 B where the valve acceleration is kept constant at a zero value in correspondence with the linear section  121 B of the valve speed curve  121 . 
     FIG. 4  is a diagram explanatory of operation of the examples of the valve lift curves of the valve-opening cam and valve-closing cam of the present invention. More specifically, (a) and (c) of  FIG. 4  show, as inventive examples, the cam rotation angel ranges α 1 -α 2  and α 4 -α 5  in the present invention, and (b) and (d) show, as comparative examples, sections centered around cam rotation angles θ 1  and θ 3  of the valve lift curves  301  and  306  of  FIG. 13 . 
   In the inventive example shown in (a) of  FIG. 4 , the valve lift curves  101  and  111  are regarded as the cam groove section  42  shown in  FIG. 1 ; more specifically, in (a) of  FIG. 4 , the valve lift curve  101  is considered to be the valve-opening cam  44  while the valve lift curve  111  is considered to be the valve-closing cam  45 , and the follower  22   a  of the rocker arm  22  of  FIG. 1  is represented by hatched circular marks. Whereas, in effect, the follower  22   a  moves in a direction substantially normal to the cam groove section  42  (i.e., perpendicular to the sheet of the figure) as the cam groove section  42  moves, let it be assumed here, for convenience of description, that the valve lift curves  101  and  111  are kept stationary and the follower  22   a  moves between the valve lift curves  101  and  111 . 
   Once the follower  22   a  reaches the inflexion point  103  while sliding along the valve lift curve  101  of the valve-opening cam  44  as indicated by arrows, it moves away from the inflexion point  103  at the jumping speed V 1  (see  FIG. 3 ) but continues to move, by an inertial force, along a tangential line  101 T at the inflexion point  103  so that it lands on a point  111 L of the linear portion  111 A of the valve lift curve  111 . 
   In the comparative example shown in (b) of  FIG. 4 , the valve lift curves  301  and  306  are regarded as a cam groove section; more specifically, in (b) of  FIG. 4 , the valve lift curve  301  is considered to be the valve-opening cam while the valve lift curve  306  is considered to be the valve-closing cam. Let it be assumed here, for convenience of description, that the follower  22   a  moves between the valve lift curves  301  and  306 . 
   Once the follower  22   a  reaches the inflexion point  302  while sliding along the valve lift curve  301  of the valve-opening cam as indicated by arrows, it moves away from the inflexion point  302  at the jumping speed VU (see  FIG. 13 ) but continues to move, by an inertial force, along a tangential line  301 T at the inflexion point  302  so that it lands on a point  306 L of the valve lift curve  306 . 
   In the inventive example shown in (c) of  FIG. 4 , once the follower  22   a  reaches an inflexion point  116  while sliding along the valve lift curve  111  of the valve-closing cam  45  as indicated by arrows, it moves away from the inflexion point  116  at the jumping speed V 2  (see  FIG. 3 ) but continues to move, by an inertial force, along a tangential line  111 T at the inflexion point  116  so that it lands on a point  101 L of the linear portion  101 B. 
   In the comparative example shown in (d) of  FIG. 4 , once the follower  22   a  reaches the inflexion point  308  while sliding along the valve lift curve  306  of the valve-closing cam as indicated by arrows, it moves away from the inflexion point  308  at the jumping speed VL (see  FIG. 13 ) but continues to move, by an inertial force, along a tangential line  306 T at the inflexion point  308  so that it lands on a point  301 L of the valve lift curve  301 . 
   More specifically, the following operation takes place in the inventive example shown in (a) of  FIG. 4  and in the comparative example shown in (b) of  FIG. 4 . In the comparative example shown in (b) of  FIG. 4 , the follower  22   a  moves away from the valve lift curve  301  at the inflexion point  302 , which means that the follower  22   a  leaves the valve lift curve  301  at the maximum valve speed point. Thus, the follower  22   a  leaves the valve lift curve  301  at the maximum jumping speed VU and then lands on the valve lift curve  306  while almost maintaining the same jumping speed VU. But, actually, during the time that the follower  22   a  leaves the valve lift curve  301  and lands on the valve lift curve  306 , the speed of the valve lift curve  306  (namely, valve speed of the valve-closing cam) gradually decreases, and the landing speed, at which the follower  22   a  lands on the valve lift curve  306  at a point where the cam rotation angle has advanced from the angle α 2 , is considerably lower than the jumping speed VU as seen in  FIG. 13 . Thus, the difference ΔVU between the jumping speed and the landing speed, i.e. the speed (colliding speed) at which the follower  22   a  collides against the valve lift curve  306  increases, which would thus result in an increased colliding impact. 
   Further, the follower  22   a  lands on the valve lift curve  306  at a great incidence angle θi 11 , and thus, a valve speed component of the follower  22   a , perpendicular to the colliding surface of the valve lift curve  306 , increases, which would also increase the colliding impact. 
   By contrast, in the inventive example shown in (a) of  FIG. 4 , where the follower  22   a  leaves the valve lift curve  101  at the inflexion point  103  where the cam rotation angle is smaller than that at the inflexion point  302  in the comparative example ((b) of  FIG. 4 ), the jumping speed V 1  (see  FIG. 3 ) of the follower  22   a  is smaller than the jumping speed in the comparative example. The follower  22   a  lands on the linear portion  111 A of the valve lift curve  111  with the same jumping speed V 1  maintained almost throughout the movement of the follower  22   a . Actually, however, the speed of the valve lift curve  111  (namely, valve speed of the valve-closing speed  45 ) changes during the time that the follower  22   a  jumps away from the valve lift curve  101  and lands on the valve lift curve  111 , and thus, when the follower  22   a  lands on the linear portion  111 A at the point preceding the point of the cam rotation angle α 2 , the landing speed of the follower  22   a  merely becomes slightly lower than the jumping speed, so that the difference ΔV 1  between the jumping speed and the landing speed, i.e. the speed (colliding speed) at which the follower  22   a  collides against the linear portion  111 A is reduced as compared to that in the comparative example shown in (b) of  FIG. 4 ; as a consequence, the colliding impact and hence sound noise can be significantly reduced. 
   Further, the follower  22   a  lands on the linear portion  111 A of the valve lift curve  111  at an incidence angle θi 1  smaller than the incidence angle θi 11  in the comparative example shown in (b) of  FIG. 4 , and thus, the valve speed component of the follower  22   a , perpendicular to the colliding surface of the valve lift curve  111 , can be reduced as compared to that in the comparative example, which can also lower the colliding impact as compared to the comparative example. 
   The cam rotation angle range α 1 -α 2  in the aforementioned example will hereinafter be referred to as “first shift section” because the follower  22   a  shifts from the valve lift curve  101  to the valve lift curve  111 . 
   Similar operation takes place in the inventive example shown in (c) of  FIG. 4  and in the comparative example shown in (d) of  FIG. 4 . Namely, in the comparative example shown in (d) of  FIG. 4 , the follower  22   a  moves away from the valve lift curve  306  at the inflexion point  308 , which means that the follower  22   a  leaves the valve lift curve  306  at a point where the absolute value of the valve speed is maximum as shown in  FIG. 13 . Thus, the absolute value of the jumping speed VL of the follower  22   a  becomes maximum, and the follower  22   a  then lands on the valve lift curve  301  while almost maintaining the jumping speed VL. But, actually, during the time that the follower  22   a  leaves the valve lift curve  306  and lands on the valve lift curve  301 , the speed of the valve lift curve  301  (namely, valve speed of the valve-opening cam) gradually decreases, and the absolute value of the landing speed, at which the follower  22   a  lands on the valve lift curve  301  at a point where the cam rotation angle has advanced from the angle α 5 , is considerably lower than the absolute value of the jumping speed VL as seen in  FIG. 13 . Thus, the difference ΔVL between the absolute values of the jumping speed and landing speed, i.e. the speed (colliding speed) at which the follower  22   a  collides against the valve lift curve  301  increases which would result in an increased colliding impact. 
   Further, the follower  22   a  lands on the valve lift curve  301  at a great incidence angle θi 12 , and thus, a valve speed component of the follower  22   a , perpendicular to the colliding surface of the valve lift curve  301 , increases, which would also increase the colliding impact. 
   By contrast, in the inventive example shown in (c) of  FIG. 4 , where the follower  22   a  leaves the valve lift curve  111  at the inflexion point  116  where the cam rotation angle is smaller than that at the inflexion point  308  in the comparative example ((b) of  FIG. 4 ), the absolute value of the jumping speed V 2  is smaller than the absolute value of the jumping speed in the comparative example. The follower  22   a  lands on the linear portion  101 B of the valve lift curve  101  with the same jumping speed V 2  almost maintained throughout the movement of the follower  22   a . Actually, however, the speed of the valve lift curve  101  (namely, valve speed of the valve-opening speed  44 ) changes during the time that the follower  22   a  jumps away from the valve lift curve  111  and lands on the valve lift curve  101 , and thus, when the follower  22   a  lands on the linear portion  101 B at the point preceding the cam rotation angle α 5 , the landing speed of the follower  22   a  merely becomes slightly lower than the jumping speed, so that the difference ΔV 2  between the jumping speed and the landing speed, i.e. the speed (colliding speed) at which the follower  22   a  collides against the linear portion  101 B is reduced as compared to that in the comparative example shown in (d) of  FIG. 4 ; as a consequence, the colliding impact and hence sound noise can be significantly reduced. 
   Further, the follower  22   a  lands on the linear portion  101 B of the valve lift curve  101  at an incidence angle θi 2  smaller than an incidence angle θi 12  in the comparative example shown in (d) of  FIG. 4 , and thus, the valve speed component of the follower  22   a , perpendicular to the colliding surface, can be reduced as compared to that in the comparative example, which can also lower the colliding impact as compared to the comparative example. 
   The cam rotation angle range α 4 -α 5  in the aforementioned example will hereinafter be referred to as “second shift section” because the follower  22   a  shifts from the valve lift curve  111  to the valve lift curve  101 . 
     FIG. 5  is a graph showing other examples of the valve lift amounts, valve speed and valve acceleration related to the valve-opening and valve-closing cams of the present invention, for example, in the case where the air intake valve  12  is opened and closed via the valve-opening cam  44  and valve-closing cam  45  of  FIG. 1 . In  FIG. 5 , the same elements as in  FIG. 13  are indicated by the same reference characters as used in  FIG. 13  and will not be described in detail. In  FIG. 5 , the vertical axis represents the valve lift amounts, valve speeds determined by one of the valve lift amounts and valve acceleration determined by the valve speed, while the horizontal axis represents the cam rotation angles. 
   The valve lift curve  131  of the valve-opening cam is different from the valve lift curve  301  of  FIG. 13  in that it has modified portions, i.e. second-order curved portions  131 A and  131 B, in the cam rotation angle range α 1 -α 2  (i.e., first shift section) and in the cam rotation angle range α 4 -α 5  (i.e., second shift section). These second-order curved portions  131 A and  131 B have, at their opposite ends, inflexion points  133  and  134  and inflexion points  136  and  137 , respectively. 
   The valve lift curve  141  of the valve-closing cam is different from the valve lift curve  306  of  FIG. 13  in that it has modified portions, i.e. second-order curved portions  141 A and  141 B in the cam rotation angle range α 1 -α 2  and in the cam rotation angle range α 4 -α 5 . These second-order curved portions  141 A and  141 B have, at their opposite ends, inflexion points  143  and  144  and inflexion points  146  and  147 , respectively. The above-mentioned second-order curved portions  131 A and  141 A are parallel to each other, and the second-order curved portions  131 B and  141 B are parallel to each other. 
   The above-mentioned cam rotation angle range α 1 -α 2  is a range where the inflexion points  302  and  307  of the valve lift curves  301  and  306  of  FIG. 13  are included, and the above-mentioned cam rotation angle range α 4 -α 5  is a range where the inflexion points  303  and  308  of the valve lift curves  301  and  306  of  FIG. 13  are included. 
   The cam rotation angle range α 1 -α 2  in the valve speed curve  151  obtained by differentiating the valve lift curve  131  or  141  is in the form of a slanted linear section  151 A, and the cam rotation angle range α 4 -α 5  in the valve speed curve  151  is in the form of a slanted linear section  151 B. 
   The slanted linear section  151 A is a portion where the valve speed is lower than the peak of the valve speed curve  151 , i.e. lower than the maximum speed point  312  of the valve speed curve  311  ( FIG. 13 ) and where the valve speed gradually decreases at a predetermined rate. 
   The slanted linear section  151 B is a portion where the absolute value of the valve speed is lower than the peak in the negative-speed region of the valve speed curve  151 , i.e. lower than the minimum speed point (i.e., peak in the negative-speed region)  314  of the valve speed curve  311  ( FIG. 13 ) and where the absolute value of the valve speed gradually decreases at a predetermined rate. 
   In  FIG. 5 , reference numeral  153  represents a jumping point at which the follower (i.e., follower  22   a  ( FIG. 1 ) or end section  62 A ( FIG. 2 )) moves away from (i.e., disengages from) the cam surface of the valve-opening cam. The jumping point is located at the cam rotation angle α 1  of the valve speed curve  151 , and is a peak point where the valve speed takes the greatest value V 3  in the positive-speed region of the valve speed curve  151 . Further, reference numeral  154  represents a landing point where the follower lands on the valve-closing cam surface and which is located on the horizontal linear section  151 A. These jumping point  153  and landing point  154  will be later explained in greater detail with reference to  FIG. 6 . 
   Difference between a jumping speed of the follower (valve speed) at the jumping point  153  and a landing speed of the follower (valve speed) at the landing point  154  is indicated by ΔV 3 . 
   In the instant embodiment, the valve speed at the jumping point  153  is set to be lower than the valve speed at the jumping point  312  (see also  FIG. 13 ) and the valve speed at the landing point  154  is set to be higher than the valve speed at the landing point  316  (see also  FIG. 13 ), so that the speed difference ΔV 3  is smaller than the speed difference ΔVU. 
   Similarly, in  FIG. 5 , reference numeral  157  represents a jumping point at which the follower moves away from the cam surface of the valve-closing cam. This jumping point is located at the point of the cam rotation angle α 4  on the valve speed curve  151 , and it is a peak point where the absolute value of the valve speed takes the greatest value V 4  in the negative-speed region of the valve speed curve  151 . Further, reference numeral  158  represents a landing point where the follower lands on the valve-opening cam surface and which is located on the slanted linear section  151 B. These jumping point  157  and landing point  158  will be later explained in greater detail with reference to  FIG. 6 . 
   Difference between a jumping speed of the follower at the jumping point  157  and a landing speed of the follower at the landing point  158  is indicated by ΔV 4 . 
   In the instant embodiment, the absolute value of the valve speed at the jumping point  157  is set to be smaller than the absolute value of the valve speed at the jumping point  314  (see also  FIG. 13 ) and the absolute value of the valve speed at the landing point  158  is set to be higher than the absolute value of the valve speed at the landing point  318  ( FIG. 13 ), so that the speed difference ΔV 4  is smaller than the speed difference ΔVL. 
   The valve acceleration curve  155  obtained by differentiating the valve speed curve  151  has, in the cam rotation angle range α 1 -α 2 , a linear section  155 A where the valve acceleration is kept constant at a negative value in correspondence with the linear section  151 A of the valve speed curve  151 , and has, in the cam rotation angle range α 4 -α 5 , a linear section  155 B where the valve acceleration is kept constant at a positive value in correspondence with the linear section  151 B of the valve speed curve  151 . 
     FIG. 6  is a diagram explanatory of operation of the other examples of the valve lift curves of the valve-opening cam and valve-closing cam of the present invention. More specifically, (a) and (c) of  FIG. 6  show the cam rotation angel ranges α 1 -α 2  and α 4 -α 5  in enlarged scale, and (b) and (d) show, as comparative examples, sections centered around cam rotation angles θ 1  and θ 3  of the valve lift curves  301  and  306  of  FIG. 13 . 
   In the inventive example shown in (a) of  FIG. 6 , the valve lift curves  131  and  141  are regarded as the cam groove section  42  shown in  FIG. 1 ; more specifically, in (a) of  FIG. 6 , the valve lift curve  131  is considered to be the valve-opening cam  44  while the valve lift curve  141  is considered to be the valve-closing cam  45 , and the follower  22   a  of the rocker arm  22  of  FIG. 1  is represented by hatched circular marks. Whereas, in effect, the follower  22   a  moves in the direction substantially normal to the cam groove section  42  (i.e., perpendicular to the sheet of the figure) as the cam groove section  42  moves, let it be assumed here, for convenience of description, that the valve lift curves  131  and  141  are kept stationary and the follower  22   a  moves between the valve lift curves  131  and  141 . 
   Once the follower  22   a  reaches the inflexion point  133  while sliding along the valve lift curve  131  of the valve-opening cam  44  as indicated by arrows, it moves away from the inflexion point  133  at the jumping speed V 3  (see  FIG. 5 ) but continues to move, by an inertial force, along a tangential line  131 T at the inflexion point  133  so that it lands on the portion  141 A of the valve lift curve  141 . In the figure, reference numeral  141 L represents a landing point of the portion  141 A, and  141 S represents a tangential line at the landing point  141 L. 
   In the comparative example shown in (b) of  FIG. 6 , once the follower  22   a  reaches the inflexion point  302  while sliding along the valve lift curve  301  of the valve-opening cam as indicated by arrows, it moves away from the inflexion point  302  but continues to move along the tangential line  301 T at the inflexion point  302  so that it lands on the landing point  306 L of the valve lift curve  306 . 
   In the inventive example shown in (c) of  FIG. 6 , once the follower  22   a  reaches the inflexion point  146  while sliding along the valve lift curve  141  of the valve-closing cam  45  as indicated by arrows, it moves away from the inflexion point  146  at the jumping speed V 4  (see  FIG. 5 ) but continues to move, by an inertial force, along a tangential line  141 T at the inflexion point  146  so that it lands on the second-order curved portion  131 B. In the figure, reference numeral  131 L represents a landing point of the second-order curved portion  131 B, and  131 S represents a tangential line at the landing point  131 L. 
   In the comparative example shown in (d) of  FIG. 6 , once the follower  22   a  reaches the inflexion point  308  while sliding along the valve lift curve  306  of the valve-closing cam as indicated by arrows, it continues to move along the tangential line  306 T at the inflexion point  308  so that it lands on the point  301 L of the valve lift curve  301 . 
   More specifically, the following operation takes place in the inventive example shown in (a) of  FIG. 6  and in the comparative example shown in (b) of  FIG. 6 . In the comparative example shown in (b) of  FIG. 6 , the difference ΔVU between the jumping speed of the follower  22   a  at the inflexion point  302  and the landing speed of the follower  22   a  at the landing point  306 L is great, so that the follower  22   a  collides against the valve lift curve  306  with a great impact force. Further, the follower  22   a  lands on the valve lift curve  306  at a great incidence angle θi 11 , and thus, a valve speed component of the follower  22   a , perpendicular to the colliding surface, increases, which would also increase the colliding impact. 
   By contrast, in the inventive example shown in (a) of  FIG. 6 , where the follower  22   a  leaves the valve lift curve  131  at the inflexion point  133  where the cam rotation angle is smaller than that at the inflexion point  302  in the comparative example ((b) of  FIG. 6 ), the jumping speed V 3  (see  FIG. 5 ) of the follower  22   a  is smaller than the jumping speed in the comparative example. The follower  22   a  lands on the second-order curved portion  141 A with the same jumping speed V 3  almost maintained throughout the movement of the follower  22   a . Actually, however, the speed of the valve lift curve  141  (namely, valve speed of the valve-closing speed  45 ) changes during the time that the follower  22   a  jumps away from the valve lift curve  131  and lands on the valve lift curve  141 , and thus, when the follower  22   a  lands on the second-order curved portion  141 A at the point preceding the point of the cam rotation angle α 2 , the landing speed of the follower  22   a  merely becomes slightly lower than the jumping speed as seen in  FIG. 5 , so that the difference ΔV 3  between the jumping speed and the landing speed, i.e. the colliding speed at which the follower  22   a  collides against the second-order curved portion  141 A is reduced as compared to that in the comparative example shown in (b) of  FIG. 6 ; as a consequence, the colliding impact and hence sound noise can be significantly reduced. 
   Further, the follower  22   a  lands on the second-order curved portion  141 A of the valve lift curve  111  at an incidence angle θi 3  smaller than the incidence angle θi 11  in the comparative example shown in (b) of  FIG. 6 , and thus, the valve speed component of the follower  22   a , perpendicular to the colliding surface, can be reduced as compared to that in the comparative example, which can also lower the colliding impact as compared to the comparative example. 
   Similar operation takes place in the inventive example shown in (c) of  FIG. 6  and in the comparative example shown in (d) of  FIG. 6 . Namely, in the comparative example shown in (d) of  FIG. 6 , the difference ΔVL between the absolute values of the jumping speed and landing speed is great, and, due to the great difference ΔVL, the follower  22   a  would collide against the valve lift curve  301  with a great impact force. Further, the follower  22   a  lands on the valve lift curve  301  at a great incidence angle θi 12 , and thus, the valve speed component of the follower  22   a , perpendicular to the colliding surface, increases, which would also increase the colliding impact. 
   By contrast, in the inventive example shown in (c) of  FIG. 6 , where the follower  22   a  leaves the valve lift curve  141  at the inflexion point  146  where the cam rotation angle is smaller than that at the inflexion point  308  in the comparative example ((b) of  FIG. 6 ), the jumping speed V 4  of the follower  22   a  is smaller than the jumping speed in the comparative example. The follower  22   a  lands on the second-order curved portion  131 B with the same jumping speed V 4  almost maintained throughout the movement of the follower  22   a . Actually, however, the speed of the valve lift curve  131  (namely, valve speed of the valve-opening speed  44 ) changes during the time that the follower  22   a  jumps away from the valve lift curve  141  and lands on the valve lift curve  131 , and thus, when the follower  22   a  lands on the second-order curved portion  131 B at the point preceding the cam rotation angle α 5 , only the absolute value of the landing speed of the follower  22   a  becomes slightly lower than the jumping speed, so that the difference ΔV 4  between the jumping speed and the landing speed, i.e. the speed (colliding speed) at which the follower  22   a  collides against the second-order curved portion  131 B is reduced as compared to that in the comparative example shown in (d) of  FIG. 6 ; as a consequence, the colliding impact and hence sound noise can be significantly reduced. Further, the follower  22   a  lands on the second-order curved portion  131 B at an incidence angle θi 4  smaller than the incidence angle θi 12  in the comparative example shown in (d) of  FIG. 6 , and thus, the valve speed component of the follower  22   a , perpendicular to the colliding surface, can be reduced as compared to that in the comparative example, which can also lower the colliding impact as compared to the comparative example. 
     FIG. 7  is a diagram explanatory of a former half of an operational sequence of a process for setting cam profiles of the valve-opening cam and valve-closing cam according to the present invention. 
   First step of the cam-profile setting process shown in (a) of  FIG. 7  creates, on the basis of basic specifications of the internal combustion engine, the basic valve lift curve  301  and the basic valve speed curve  311  by differentiating the basic valve lift curve  301 . Cam rotation angle range over which the valve is opened will be referred to as “basic opening cam angle”. 
   Second step of the cam-profile setting process shown in (b) of  FIG. 7  creates, for example, improved valve speed curves  241 A and  241 B each including a portion that has a speed difference (ultimate valve speed difference) ΔV 1  smaller than a speed difference (basic valve speed difference) ΔVU in the basic valve speed curve  311  (see (a) of  FIG. 7 ). Cam rotation angle range in the improved valve speed curves  241 A over which the valve is opened will be referred to as “opening cam angle A”, and a cam rotation angle range in the improved valve speed curves  241 B over which the valve is opened will be referred to as “opening cam angle B”. 
   Third step of the cam-profile setting process shown in (c) of  FIG. 7  creates an ultimate valve speed curve  121  by adjusting an integrated valve speed value of the improved valve speed curves  241 A and  241 B to agree with or approach an integrated valve speed value of the basic valve speed curve  311 . At this step, another operation is also performed for adjusting the opening cam angles A and B to the basic opening cam angle. 
   That the integrated valve speed value of the improved valve speed curves  241 A and  241 B agrees with or approach the integrated valve speed value of the basic valve speed curve  311  means that a difference between the integrated valve speed value of the basic valve speed curve  311  and the integrated valve speed value of the improved valve speed curves  241 A and  241 B falls within a range of 0-10% of the integrated valve speed value of the basic valve speed curve  311 . 
     FIG. 8  is a diagram explanatory of a latter half of the operational sequence of the process for setting cam profiles of the valve-opening cam and valve-closing cam of the present invention. 
   Fourth step of the cam-profile setting process shown in (a) of  FIG. 8  creates, for example, an ultimate valve lift curve  101  of the valve-opening cam by integrating the above-mentioned ultimate valve speed curve  121 . Note that an ultimate valve lift curve of the valve-closing cam is created on the basis of a combination of the ultimate valve lift curve  101  of the valve-opening cam and a valve lift amount difference therefrom. 
   Fifth step of the cam-profile setting process shown in (b) of  FIG. 8  determines cam profiles of the valve-opening cams  44  and  81  and valve-closing cams  45  and  82  on the basis of a combination of the ultimate valve lift curve  101  ((a) of  FIG. 8 ) and specifications of the rocker arms. 
     FIG. 9  is a diagram showing first modifications of the valve lift curves of the valve-opening and valve-closing cams, in which the vertical axis represents the valve lift amounts while the horizontal axis represents the cam rotation angles. 
   In the figure, reference character  161  indicates a valve lift curve of the valve-opening cam having a middle curve section of a high mountain shape, which represents a modification of the valve lift curve  101  shown in  FIG. 3 . Reference character  171  indicates a valve lift curve of the valve-closing having a middle curve section of a high mountain shape, which represents a modification of the valve lift curve  111  shown in  FIG. 3 . Cam rotation angle range β 3 -β 4  corresponds to the cam rotation angle range α 1 -α 2  of  FIG. 3 , cam rotation angle β 6  corresponds to the cam rotation angle α 3  of  FIG. 3 , and cam rotation angle range β 8 -β 9  corresponds to the cam rotation angle range α 4 -α 5  of  FIG. 3 . 
   The valve lift curve  161  includes a first basic lift section  162  in the cam rotation angle range β 1 -β 4 , linear second connection section  163  in the cam rotation angle range β 4 -β 5 , great list section  164  in the cam rotation angle range β 5 -β 7 , linear third connection section  166  in the cam rotation angle range β 7 -β 8 , and second basic lift section  167  in the cam rotation angle range β 8 -β 11 . The first basic lift section  162  and second basic lift section  167  correspond to a part of the valve lift curve  101  shown in  FIG. 3 . The first basic lift section  162  includes a linear portion  101 A, and the second basic lift section  167  includes a linear portion  101 B. 
   The valve lift curve  171  includes a first correction ramp section  172  in the cam rotation angle range β 1 -β 2 , linear first connection section  173  in the cam rotation angle range β 2 -β 3 , basic lift section  174  in the cam rotation angle range β 3 -β 9 , linear fourth connection section  176  in the cam rotation angle range β 9 -β 10 , and second correction ramp section  177  in the cam rotation angle range β 10 -β 11 . The basic lift section  174  corresponds to a part of the valve lift curve  111  shown in  FIG. 3 . The basic lift section  174  is a part of the valve lift curve  111  and includes linear portions  11 A and  111 B. 
   The cam rotation angle includes: a first ramp section in the cam rotation angle range β 1 -β 3  including mountain base portions of the valve lift curves  161  and  171 ; first shift section in the cam rotation angle range β 3 -β 4  including mountain hillside portions of the valve lift curves  161  and  171 ; great lift section in the cam rotation angle range β 4 -β 8  including maximum lift points  168  and  309  that are peaks of the valve lift curves  161  and  171  and neighborhoods of the maximum lift points  168  and  309 ; second shift section in the cam rotation angle range β 8 -β 9  including mountain hillside portions of the valve lift curves  161  and  171 ; and second ramp section in the cam rotation angle range β 9 -β 11  including the other mountain base portions of the valve lift curves  161  and  171 . 
   The valve lift curve  161  includes a second connection section in the cam rotation angle range β 4 -β 5 , and a third connection section in the cam rotation angle range β 7 -β 8 . The valve lift curve  171  includes a first connection section in the cam rotation angle range β 2 -β 5 , and a fourth connection section in the cam rotation angle range β 9 -β 10 . 
   Clearance CA between the above-mentioned first basic lift section  162  of the valve lift curve  161  and the first correction ramp section  172  of the second valve lift curve  171 , clearance CB between the above-mentioned second basic lift section  167  and the second correction ramp section  177  and clearance CD between the above-mentioned great lift section  164  and the basic lift section  174  are each set, for example, at 0.5 mm (i.e., CA=CB=CD=0.5 mm). 
   Namely, because the clearances CA, CB and CD between the valve lift curve  161  of the valve-opening cam and the valve lift curve  171  of the valve-closing cam are set to be greater than a clearance CC in the other sections than the first shift section and the second shift section of the cam rotation angle, it is not necessary to enhance the machining or manufacturing accuracy of the cam surfaces of the valve-opening and valve-closing cams except for cam surfaces corresponding to the first and second shift sections and the machining or manufacturing accuracy of component parts disposed between the cam surfaces and the air intake and exhaust valves, with the result that component parts, including the cam shaft, of the valve operation system can be reduced significantly. 
     FIG. 10  is a diagram showing second modifications of the valve lift curves of the valve-opening and valve-closing cams, in which the vertical axis represents the valve lift amounts while the horizontal axis represents the cam rotation angles, and in which the same elements as in  FIG. 13  are indicated by the same reference characters as used in  FIG. 13  and will not be described in detail to avoid unnecessary duplication. 
   In the figure, reference character  181  indicates a valve lift curve of the valve-opening cam having a middle curve section of a high mountain shape, which represents a modification of the valve lift curve  131  shown in  FIG. 5 . Reference character  191  indicates a valve lift curve of the valve-closing cam having a middle curve section of a high mountain shape, which represents a modification of the valve lift curve  141  shown in  FIG. 5 . 
   The valve lift curve  181  includes a first basic lift section  182  in the cam rotation angle range β 1 -β 4 , second connection section  163 , great lift section  164 , third connection section  166 , and second basic lift section  187  in the cam rotation angle range β 8 -β 11 . The first basic lift section  182  and second basic lift section  187  correspond to a part of the valve lift curve  131  shown in  FIG. 5 . The first basic lift section  182  includes a second-order curve portion  131 A, and the second basic lift section  187  includes a second-order curve portion  131 B. 
   The valve lift curve  191  includes a first correction ramp section  172 , first connection section  173 , basic lift section  194  in the cam rotation angle range β 3 -β 9 , fourth connection section  176 , and second correction ramp section  177 . The basic lift section  194  corresponds to a part of the valve lift curve  141  shown in  FIG. 5 . The basic lift section  194  includes second-order curve portions  141 A and  141 B. 
   Clearance CE between the above-mentioned first basic lift section  182  of the valve lift curve  181  and the first correction ramp section  172  of the second valve lift curve  191 , clearance CF between the above-mentioned second basic lift sections  187  and the second correction ramp section  177  and clearance CG between the above-mentioned great lift section  164  and the basic lift section  194  are each set at 0.5 mm (i.e., CE=CF=CG=0.5 mm). 
   Namely, because the clearances CE, CF and CG between the valve lift curve  181  of the valve-opening cam and the valve lift curve  191  of the valve-dosing cam are greater than a clearance CC in the other sections than the first shift section and the second shift section, it is not necessary to enhance the machining or manufacturing accuracy of the cam surfaces of the valve-opening and valve-closing cams except for the cam surfaces of the cams corresponding to the first second shift sections and the machining or manufacturing accuracy of component parts disposed between the cam surfaces and the air intake and exhaust valves, with the result that component parts, including the cam shaft, of the valve operation system can be reduced significantly. 
   The first and second ramp sections in the cam rotation angle include mountain base portions of the valve lift curves  181  and  191 , the first and second shift sections include mountain hillside portions of the valve lift curves  181  and  191 , and the great lift section in the cam rotation angle includes maximum lift points  188  and  309  that include peaks of the valve lift curves  181  and  191  and neighborhoods of the maximum lift points  188  and  309   
   The valve lift curve  181  also includes a second connection section in the cam rotation angle range β 4 -β 5 , and a third connection section in the cam rotation angle range β 7 -β 8 . The valve lift curve  191  also includes a first connection section in the cam rotation angle range β 2 -β 3 , and a third connection section in the cam rotation angle range β 7 -β 8 , and a fourth connection section in the cam rotation angle range β 9 -β 10 . 
     FIG. 11  is a diagram showing third modifications of the valve lift curves of the valve-opening and valve-closing cams, in which the vertical axis represents the valve lift amounts while the horizontal axis represents the cam rotation angles, and in which the same elements as in  FIG. 13  are indicated by the same reference characters as used in  FIG. 13  and will not be described in detail to avoid unnecessary duplication. 
   Normal valve lift curve  201  of the valve-opening cam is different from the valve lift amount curve  301  of the valve-opening cam shown in  FIG. 13  in that the valve lift amount in most of the cam rotation angle range θ 1 -θ 3  is offset from the corresponding section of the curve  301  in a valve-lift-amount decreasing direction. The normal valve lift curve  201  generally comprises a first ramp curve  202  in a cam rotation angle range smaller than θ 1 , a great lift correction curve  203  in the cam rotation angle range θ 1 -θ 3 , and a second ramp curve  204  in a cam rotation angle range greater than θ 3 . 
   The first and second ramp curves  202  and  204  overlap the valve lift amount curve  301  shown in  FIG. 13 . The great lift correction curve  203  includes an intermediate curve section  206 , and connecting curve sections  207  and  208  connected to the opposite ends of the intermediate curve section  206 . 
   Normal valve lift curve  211  of the valve-closing cam is different from the valve lift amount curve  306  of the valve-closing cam shown in  FIG. 13  in that the valve lift amounts in most of the cam rotation angle range smaller than θ 1  and in most of the cam rotation angle range greater than θ 3  are offset from the corresponding sections of the curve  306  in a valve-lift-amount increasing direction. The normal valve lift curve  211  generally comprises a first ramp correction curve  212  in the cam rotation angle range smaller than θ 1 , a great lift curve  213  in the cam rotation angle range θ 1 -θ 3 , and a second ramp correction curve  214  in the cam rotation angle range greater than θ 3 . 
   The first ramp correction curve  212  includes an end curve section  216  offset from a corresponding part of the valve lift amount curve  306  shown in  FIG. 13 , and a connecting curve section  217  connecting the end curve section  216  and the great lift curve  213 . The great lift curve  213  overlap a corresponding part of the valve lift amount curve  306  shown in  FIG. 13 . The second ramp correction curve  204  includes an end curve section  218  offset from a corresponding part of the valve lift amount curve  306  shown in  FIG. 13 , and a connecting curve section  219  connecting the end curve section  218  and great lift curve  213 . 
   As shown in (b) and (d) of  FIG. 4 , the follower  22   a  slides along the valve lift curve  301  until the cam rotation angle reaches θ 1  is reached, jumps away from the valve lift curve  301  at the inflexion point  302 , and lands on the valve lift curve  306  to slide therealong. Then, the follower  22   a  jumps away from the valve lift curve  306  at the inflexion point  308  at the cam rotation angle α 3 , and lands on the valve lift curve  301 . 
   Namely, the cam rotation angle range θ 1 -θ 3  of the valve lift curve  301 , and the cam rotation angle range below the angle θ 1  and cam rotation angle range above the angle θ 3  of the valve lift curve  306  are ranges where the follower  22   a  does not slide. 
   Referring back to  FIG. 11 , the curve in the cam rotation angle range θ 1 -θ 3  of the valve lift curve  301  will be referred to as “no-load curve section  331  of the valve-opening cam”, the curve in the cam rotation angle range below the angle θ 1  of the valve lift curve  306  as “no-load curve section  332  of the valve-closing cam”, and the curve in the cam rotation angle range above the angle θ 3  of the valve lift curve  306  as “no-load curve section  333  of the valve-closing cam. 
   Thus, it may be said that the intermediate curve section  206  is formed by offsetting most of the no-load curve section  331  in the valve-lift-amount decreasing direction, the end curve section  216  is formed by offsetting most of the no-load curve section  332  in the valve-lift-amount increasing direction and the end curve section  218  is formed by offsetting most of the no-load curve section  333  in the valve-lift-amount increasing direction. 
   At the jumping point  312  and landing point  316  of the valve speed curve (basic valve speed curve)  311  of the valve-opening cam shown in  FIG. 13 , the follower jumps out at the inflexion point  302  of the valve lift curve  301  and lands at the landing point  306 L (see (b) of  FIG. 4 ), and thus, the follower slides over the valve-opening cam surface in the cam rotation angle range below the cam rotation angle θ 1  at the inflexion point  302 , and slides over the valve-dosing cam surface in the cam rotation angle range above the cam rotation angle at the inflexion point  306 L. 
   Namely, according to the present invention, in the cam rotation angle range where the follower slides, one of the valve lift curves  301  and  306 , along which the follower slides, is used as-is. But, in the cam rotation angle range where the follower does not slide, the great valve lift correction curve  203 , first ramp correction curve  212  and second ramp correction curve  214  are set as no-load valve lift slide curves by one of the valve lift curves  301  and  306  along which the follower does not slide being offset away from the other of the valve lift curves  306  and  301 , the normal valve lift curve  201  of the valve-opening cam is set with the first ramp curve  202 , great lift correction curve  203  and second ramp curve  204 , and the cam profile of the valve-opening cam is determined on the basis of the normal valve lift curve  201 ; in addition, the normal valve lift curve  211  of the valve-closing cam is set with the first ramp correction curve  212 , great lift curve  213  and second ramp correction curve  214 , and the cam profile of the valve-closing cam is determined on the basis of the normal valve lift curve  211 . 
   Namely, because the no-load-side basic valve lift curve section, along which the follower does not slide, is offset away from the other basic valve lift curve, the present invention can increase the clearance between the normal valve lift curves of the valve-opening and valve-closing cams, to thereby reduce viscosity resistance and agitation resistance of lubricating oil between the cam of the non-sliding side and the corresponding follower and greatly reduce friction between the cam and the sliding portion of the follower. 
   Further, no high dimensional accuracy is required of the follower and cam of the non-sliding side; namely, no high-accuracy management is required of the clearance between the valve-opening cam and the valve-closing cam, so that it is possible to eliminate the need for enhancing the cam manufacturing accuracy and assembling accuracy and thus achieve significant cost reduction. 
     FIG. 12  is a diagram showing fourth modifications of the valve lift curves of the valve-opening and valve-closing cams, in which the vertical axis represents the valve lift amounts while the horizontal axis represents the cam rotation angles, and in which the same elements as in  FIG. 13  are indicated by the same reference characters as used in  FIG. 13  and will not be described in detail to avoid unnecessary duplication. 
   Normal valve lift curve  221  of the valve-opening cam has, in the cam rotation angle range θ 1 -θ 3 , a section modified, relative to the valve lift curve  301  of the valve-opening cam shown in  FIG. 13 , into a shape such that the modified section is smaller in valve lift amount than the corresponding section of the curve  301 . Specifically, the normal valve lift curve  221  comprises a first ramp curve  202  in the cam rotation angle range below θ 1 , a middle correction curve  223  in the cam rotation angle range θ 1 -θ 3 , and a second ramp curve  204  in the cam rotation angle range above θ 3 . 
   The middle correction curve  223  may be any desired curve, such as an algebraic curve that can be expressed easily with a mathematical expression, or a free curve that has continuity and is difficult to express with a mathematical expression. 
   Normal valve lift curve  231  of the valve-dosing cam has, in the cam rotation angle range below θ 1  and cam rotation angle range above θ 3 , sections modified, relative to the valve lift curve  306  of the valve-closing cam, into a shape such that the modified sections are greater in valve lift amount than the corresponding sections of the curve  306  shown in  FIG. 13 . Specifically, the normal valve lift curve  231  comprises an end correction curve  232  in the cam rotation angle range below θ 1 , a great lift curve  213  in the cam rotation angle range θ 1 -θ 3 , and an end correction curve  234  in the cam rotation angle range above θ 3 . 
   The end correction curves  232  and  234  may each be any desired curve, such as an algebraic curve that can be expressed easily with a mathematical expression, or a free curve that has continuity and is difficult to express with a mathematical expression. 
   As described above in relation to  FIGS. 1 ,  11  and  12 , the valve-opening and valve-closing cams  44  and  45 , which forcibly drive the air intake valve  12  and exhaust valve  13 , are characterized by having their respective cam profiles set by: plotting, in a graph where the vertical axis represents the valve lift amounts of the air intake valve  12  and exhaust valve  13  and the horizontal axis represents the cam rotation angles, the basic valve lift curve  301  of the valve-opening cam  44  indicative of relationship between the cam rotation angles and valve lift amounts of the valve-opening cam  44  and the basic valve lift curve  306  of the valve-closing cam  45  indicative of relationship between the cam rotation angles and valve lift amounts of the valve-closing cams  45  by offsetting the basic valve lift curve  301  of the valve-opening cam  44  in the valve-lift-amount increasing direction; setting the intermediate curve section  206 , as a no-load valve lift correction curve, by offsetting the no-load curve section  331  of the basic valve lift curve  301  of the valve-opening cam  44 , along which a corresponding one of the followers  22   a  for actuating the air intake valve  12  and exhaust valve  13  does not slide relative to the cam  44 , away from the other basic valve lift curve  306  and setting the end curve sections  216  and  218 , as no-load valve lift correction curves, by offsetting the no-load curve sections  332  and  333  of the basic valve lift curve  306  of the valve-closing cam  45 , along which the follower  22   a  does not slide relative to the cam  45 , away from the other basic valve lift curve  301 , or by modifying such offset no-load curve sections  331 ,  332  and  333  into desired shapes; and forming the normal valve lift curves  201  and  211  by connecting, as needed, the no-load valve lift correction curves with the remaining sections of the corresponding basic valve lift curves  301  and  306  via the connecting curve sections  207 ,  208 ,  217  and  219 , the cam profiles of the valve-opening and valve-closing cams  44  and  45  being set on the basis of the normal valve lift curves  201  and  211 . 
   Further, as described above in relation to  FIGS. 1 and 9 , the basic valve lift curve  101  of the valve-opening cam  44  and basic valve lift curve  111  of the valve-closing cam  45  each have a middle curve section of a high mountain shape, two cam rotation angle ranges including the mountain base portions of each of the basic valve lift curves  101  and  111  are set as the first and second ramp sections, one of the two cam rotation angle ranges including the mountain hillside portions of each of the basic valve lift curves  101  and  111 , where the follower  22   a  of the air intake valve or exhaust valve shifts from the valve-opening cam  44  to the valve-closing cam  45 , is set as the first shift section while the other of the two cam rotation angle ranges including the mountain hillside portions, where the follower  22   a  shifts from the valve-closing cam  45  to the valve-opening cam  44 , is set as the second shift section, and another cam rotation angle range including the mountain top portion of each of the basic valve lift curves  101  and  111  is set as the great lift section. Further, as shown in  FIG. 9 , the normal valve lift curve  161  of the valve-opening cam  44  is formed by connecting together, via the second and third connecting curve section sections  163  and  166 , the no-load valve lift correction curve  164  of the valve-opening cam  44 , formed by offsetting the great lift section of the basic valve lift curve  101  of the valve-opening cam  44  in the valve-lift-amount decreasing direction, the first and second shift sections of the valve lift curve  101  and the first and second ramp sections of the valve lift curve  101 , and the cam profile of the valve-opening cam  44  is set on the basis of the normal valve lift curve  161 . Similarly, the normal valve lift curve  171  of the valve-closing cam  45  is formed by connecting together, via the first and fourth connection (curve) sections  173  and  176 , the first correction ramp section  172  and second correction ramp section  177  as the no-load valve lift correction curve of the valve-closing cam  45 , formed by offsetting the first and second ramp sections of the basic valve lift curve  111  of the valve-closing cam  45  in the valve-lift-amount increasing direction, the first and second shift sections of the valve lift curve  111  and the great lift section of the curve  111 , and the cam profile of the valve-closing cam  45  is set on the basis of the normal valve lift curve  171  of the valve-closing cam  45 . 
   With the aforementioned arrangements, portions of the clearance between the normal valve lift curve  161  of the valve-opening cam  44  and the normal valve lift curve  171  of the valve-closing cam  45  can be set to increased sizes. Thus, the clearance has to be managed with high accuracy only in the first and second shift sections; namely, the clearance need not be managed with high accuracy in the other sections than the first and second shift sections. Consequently, high machining or manufacturing accuracy and assembling accuracy is required of the various component parts of the valve operating device  15 , which can thereby achieve significant cost reduction of the internal combustion engine  10 . 
   Further, with the size increase of the clearance, the viscosity resistance and agitation resistance of the lubricating oil between the valve-opening and valve-closing cams  44  and  45  and the followers  22   a  can be effectively reduced, so that the performance, such as the output and fuel efficiency, of the internal combustion engine  10  can be significantly enhanced. 
   Note that, whereas the preferred embodiment has been described above in relation to the case where the first, second, third and fourth connection sections  173 ,  162 ,  166  and  176  are formed as straight lines, the present invention is not so limited and these connection sections  173 ,  162 ,  166  and  176  may be formed as curved lines that smoothly connect to adjoining lines. 
   Further, whereas the first correction ramp section  172  in the preferred embodiment has been described above as formed by offsetting upwardly the ramp section in the cam rotation angle range β 1 -β 2  of the first basic lift section  162  and the second correction ramp section  177  has been described above as formed by offsetting upwardly the ramp section from the cam rotation angle range β 10 -β 11  of the second basic lift section  167 , the present invention is not so limited; for example, the first correction ramp section  172  may be formed continuously with the first connection section  173  with the clearance between the first connection section  173  and the first basic lift section  162  gradually increasing in size in a direction from the cam rotation angle β 3  toward the cam rotation angle β 1 , and the second correction ramp section  177  may be formed continuously with the fourth connection section  176  with the clearance between the fourth connection section  176  and the second basic lift section  167  gradually increasing in size in a direction from the cam rotation angle β 9  toward the cam rotation angle β 11 . 
   Further, as described above in relation to  FIGS. 1 ,  3  and  13 , the valve-opening and valve-closing cams  44  and  45 , which forcibly drive the air intake valve  12  and exhaust valve  13 , are characterized by having their respective cam profiles set by: plotting, in a graph where the vertical axis represents the valve lift amounts of the air intake valve  12  and exhaust valve  13  and the horizontal axis represents the cam rotation angles, the basic valve lift curve  301  of the valve-opening cam  44 , indicative of relationship between the cam rotation angles and valve lift amounts of the valve-opening cam  44 , and the basic valve lift curve  306  of the valve-closing cam  45 , indicative of relationship between the cam rotation angles and valve lift amounts of the valve-closing cams  45 ; setting the clearance CC between the basic valve lift curves  301  and  306  as a valve lift amount difference between the curves  301  and  306 ; setting, with respect to the basic valve lift curves  301  and  306 , the ultimate valve lift curves  101  and  111  of the valve-opening and valve-closing cams  44  and  45  each provided with the first shift section including a cam rotation angle range where a corresponding one of the followers  22   a  for actuating the air intake valve  12  and exhaust valve  13  jumps away from the valve-opening cam  44  and lands on the valve-closing cam  45  and the second shift section including a cam rotation angle range where the follower  22   a  jumps away from the valve-closing cam  45  and lands on the valve-opening cam  44 ; determining the basic speed difference ΔVU indicative of a difference between jumping and landing speeds of the follower  22   a  on the basic valve speed curve  311  determined from the basic valve lift curves  301  and  306  of the valve-opening and valve-closing cams  44  and  45 ; and determining the ultimate speed difference ΔV 1  indicative of a difference between jumping and landing speeds of the follower  22   a  on the ultimate valve speed curve  121  determined from the ultimate valve lift curves  101  and  111  of the valve-opening and valve-closing cams  44  and  45 , the respective cam profiles of the valve-opening and valve-closing cams  44  and  45  being set in such a manner that the ultimate speed difference ΔV 1  is smaller than the basic speed difference ΔVU. 
   With the aforementioned arrangements, it is possible to reduce the colliding speed at which the follower  22   a  collides against the valve-opening or valve-closing cam  44  or  45  in the first and second shift sections even in the case where the clearance between the lift curves  101  and  111  of the valve-opening and valve-closing cams  44  and  45 . Because the impact at the time of the collision can be lessened in this manner, the present invention can effectively minimize production of noise sound while minimizing the necessary cost. 
   Further, the cam profiles are set in such a manner that, in the first and second shift sections, the absolute value of the valve speed at the jumping point  123  as the peak of the ultimate valve speed curve  121  is set to be smaller than the absolute value of the valve speed at the maximum speed point  312  as the peak of the basic valve speed curve  311 , and that the absolute values of the landing speeds on the valve speed curve  121  in the first and second shift sections are kept at constant values corresponding to higher speed-curve positions than the corresponding absolute values of the landing speeds on the basic valve speed curve  311 ; more specifically, the absolute value of the landing speed on the valve speed curve  121  in the first shift section (i.e., positive speed region) is kept at a constant value greater than the corresponding absolute value of the landing speed of the basic valve speed curve  311 , while the absolute value of the landing speed on the valve speed curve  121  in the second shift section (i.e., negative speed region) is kept at a constant value smaller than the corresponding absolute value of the landing speed of the basic valve speed curve  311 . In this way, not only the jumping speed V 1  of the follower  22   a  on the valve speed curve  121  is limited, but also the landing speed of the follower  22   a  on the valve speed curve  121  is increased. Thus, it is possible to decrease the speed difference ΔV 1  between the jumping speed V 1  and landing speed of the follower  22   a , so that the colliding speed of the follower  22   a  against the vale-opening or valve-closing cam  44  or  45  can be reduced and thus the impact at the time of the collision can be effectively lessened. 
   Furthermore, as described above in relation to  FIGS. 1 ,  3 ,  7 ,  8  and  13 , the method for setting the cam profiles of the valve-opening and valve-closing cams  44  and  45 , which forcibly drive the air intake valve  12  and exhaust valve  13 , is characterized by comprising: the first step of plotting valve lift curves  201  and  306  on the basis of a predetermined lift amount required of the air intake valve  12  or exhaust valve  13  and a valve speed curve from the valve lift curves; the second step of determining a basic speed difference between the jumping speed VU and landing speed, on the basic speed curve  311 , of a corresponding one of the followers  22   a , provided for actuating the air intake valve  12  and exhaust valve  13 , when the follower  22   a  jumps away from the valve-opening cam  44  and lands on the valve-closing cam  45  or when the follower  22   a  jumps away from the valve-closing cam  45  and lands on the valve-opening cam  44 , and plotting improved valve speed curves  241 A and  241 B such that the speed difference ΔV 1  between the jumping speed VU and landing speed of the follower  22   a  is smaller than the speed difference ΔVU; the third step of adjusting integrated values of the valve speeds indicated by the improved valve speed curves  241 A and  241 B to integrated values of the valve speeds indicated by the valve speed curve  311  while maintaining the improved speed difference ΔV 1  and thereby obtaining the ultimate valve speed curve  121 ; and the fourth step of plotting the valve lift curves  101  and  111  on the basis of the ultimate valve speed curve  121 . 
   With the aforementioned second step, it is possible to reduce the colliding speed at which the follower  22   a  collides against the valve-opening cam  44  or valve-closing cam  45 , to thereby lessen the colliding impact. Further, with the third step, which adjusts the integrated values of the valve speeds indicated by the improved valve speed curves  241 A and  241 B to the integrated values of the valve speeds indicated by the valve speed curve  311  while maintaining the improved speed difference ΔV 1 , it is possible to cause the shape of the ultimate valve lift curve  101  to agree with or approach the shape of the valve lift curve  301 , except in a section that includes the range where the follower  22   a  jumps away from the valve-opening cam  44  and lands on the valve-closing cam  45  or where the follower  22   a  jumps away from the valve-closing cam  45  and lands on the valve-opening cam  44 . 
   The embodiment shown in  FIG. 1  has been described above as constructed so that the rocker arm  22  is driven by the cam groove  42  of the cam shaft  18 , via the follower  22   a , to open/close the air intake valve  12 , and the embodiment shown in  FIG. 2  has been described above as constructed so that the air intake valve  62  is opened/closed by the valve-opening cam  81  and valve-closing cam  82  of the cam shaft  67  via the rocker arms  73  and  74 . However, the present invention is not so limited, and the end section  62 A of the air intake valve  62  shown in  FIG. 2  may be constructed to function as a follower that slides along the cam groove  42  so that the air intake valve  62  of  FIG. 2  is opened/closed directly by the cam groove  42 . 
   The valve operating device and cam-profile setting method of the present invention are suitably applicable to forced-valve-opening/closing cams for an internal combustion engine.