Patent Publication Number: US-9897189-B2

Title: Wave speed reducer having self-locking function and compound type reducer device

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a structural arrangement technique of a reducer, particularly to a speed reducer having a self-locking function and a compound type reducer device thereof. 
     2. Description of Related Art 
     In the structural arrangement technical field of conventional reducers, the self-locking function to be studied herein meant that driving power was loaded on an active member so as to generate forward output at a specific reduction ratio from a driven follower. When no driving power was loaded on the active member to be a free end, driving power (including a driving force exerted by an external power source, a driving force from torque generated by their gravity force of the follower and its connected members) was so loaded on the follower that it could not drive the active member of the free end to reversely rotate, i.e. the so-called “self-locking”. The “self-locking” meant a mechanism generated at a tooth flank between the active member and the engaged follower except of device arrangement (for example, a driven or reciprocating level, a positioning latch or a pin), such as, events latch, etc., manufacturing cost of which increased. 
     Conventional reducers generally included a mechanism having a worm wheel driven by a worm shaft, a planetary gear, and a spin-wave driver. Only the mechanism having a worm wheel driven by a worm shaft was designed by modification of engaging angle between tooth flank of the worm shaft and tooth flank of the worm wheel so as to achieve the above self-locking objective. 
     Please refer to  FIGS. 1 and 2  which disclosed a schematic diagram showing an arrangement of conventional worm wheels and worm shafts and their lead angle. They demonstrated that a lead angle α was formed at an engaged a tooth flank between a general worm shaft  71  and a worm wheel  72 . For the worm shaft  71 , the lead angle α(the so-called friction angle) is formed by a slope formed from a worm shaft lead L and a worm shaft circumference length S. When the worm shaft  71  of the active member rotated, a positive force F was exerted from a tooth flank  71   a  of the worm shaft  71  onto a tooth flank  72   a  of the worm wheel  72  of the follower. A component force Fsinα generated in the clockwise direction of the lead angle α by using the positive force F was smaller than the friction force μ×Fcosα (μ is a frictional coefficient between the tooth flank  71   a  and the tooth flank  72   a ) generated at the tooth flanks  71   a ,  72   a  between the worm shaft  71  and the worm wheel  72 , a self-locking effect was generated. In other words, at the state of self-locking design, a reverse rotation of the worm wheel  72  forced to reversely drive the worm shaft  71  because the tooth flank  71   a  and  72   a  was engaged. An advantage of the self-locking function is that every transmission component of the reducer mechanism was protected from un-predictable reverse rotation, thus, there should be no damages or risk. 
     In addition to the above mechanism of the worm shaft driving the worm wheel, there were no self-locking mechanism mounted on the conventional planetary gears and spin-wave driver till now. Conventional spin-wave drivers and planetary gears belong to typical speed reduction gearing devices. A spin-wave driver was a speed reduction gearing device. The first spin-wave driver invented was a Harmonic® driver disclosed in U.S. Pat. No. 2,906,143 filed in 1955 by C. W. Musser. After continuous improvement, details of a spin-wave driver mechanism were disclosed in U.S. Pat. No. 5,643,128. 
     In comparison to conventional planetary gears, conventional spin-wave drivers could provide more number of teeth on engaged gears and a larger amount of gear range, therefore, conventional spin-wave drivers provided better driving accuracy and driving efficiency regarding output value of the whole ratio of reduction. 
     Furthermore, in the conventional techniques, there were no wave-motions involved in the present invention. A similar wave-motion of the prior arts was the above spin-wave driver. 
     A general conventional spin-wave driver comprised a cam (or a so-called wave generator), a plurality of rollers and a spline wheel (having specific internally toothed circular spline wheel) from inside to outside. The cam was used as a input shaft. The plurality of rollers were arranged around a location between the cam and the spline wheel. A plurality of spline apertures which could accommodate rollers to engage were arranged on the spline wheel in ring-shaped form. The cam was used to drive some of the plurality of rollers by providing input force so as to engage the corresponding spline apertures of the spline wheel in order to rotate a bearing member at a ratio of reduction. 
     Furthermore, from the contents of the patents, it can be known that every spline aperture in the conventional spin-wave drivers comprises a tilting tooth flank extending along both sides of a void between the teeth and the tooth flank and the tooth flank at both sides extents and connects to a crest of teeth at both sides. The contour shape of each spline aperture is approximately V-shaped. Some of the rollers in the conventional spin-wave driving process would engage with tooth flank of the engaged spline aperture driven by a cam surface of the cam. Then, the tooth flank of the spline aperture was used as an effective contact surface for transmitting driving force of the rollers. For example, in U.S. Pat. No. 5,643,128, it was disclosed that a bearing member (roller ring) for receiving a plurality of rollers were arranged between the cam and the spline wheel. In some embodiments, the bearing member is used as an output shaft so as to drive the bearing member to rotate at a ratio of reduction by a force provided by rollers driven and transmitted by a driving force of the cam via transmission of the tooth flank of the spline aperture. 
     From the above descriptions, it could be known that not only the tooth flank of the spline apertures could be used as an effective contacting surface for transmitting working force, but also it could be used as an effective contacting surface for providing force to the rollers from the cam. We could observe that during the spin-wave driving process, when the cam surface pushed and drove the rollers to contact the tooth flank of the spline apertures, the driven rollers moved to a displacement at a radial direction regarding to the cam axis and to an angular displacement at an angular direction surrounding the cam axis. Then, the displacements would affect whether the tooth flank could be an effective contacting surface for sufficiently or really transmitting functional force and providing force generated by the cam. The conventional spin-wave drivers could maintain good driving accuracy and driving efficiency. However, in prior arts, the contour of the disclosed spline apertures is in V-shaped form. The well-known patents did not disclose or teach or study that the techniques of forming the contour of spline apertures and the cams were capable of effectively transmitting functional force, such as, when an input shaft rotated for half a circle, the rollers would move into a next position of the spline aperture. During the procedures, the speed would become uncertain because of an unclear definition of the V-shape so that the speed of the roller moving into the next spline aperture would become unstable. The driving accuracy of the conventional spin-wave drivers regarding output end under variation of tiny rotational angle would be affected. 
     SUMMARY OF THE INVENTION 
     The objective of the present invention is to solve a problem that poor driving accuracy in view of tiny rotation angle at an output end for a conventional wave-motion mechanism is improved by using a wave speed reducer. A cam of the wave speed reducer is designed self-locking is implemented when reverse transmission occurs between the cam, a roller, a bearing member and a spline aperture so as to solve the problem of no self-locking function for the conventional wave-motion mechanism. 
     The so-called “wave speed reducer” defined in the present invention has functions of a cam, a roller, a bearing member and a spline wheel which is summarily the same as a conventional wave-motion. However, the driving waves generated by the wave speed reducer in the present invention (or the called wave-motion) are harmonic waves. 
     In order to achieve the objective and to solve the problems, a preferred embodiment of the present invention provides a wave speed reducer having a self-locking function comprising in co-axial arrangement: 
     a cam at a cam axis circumference of which being a cam periphery comprising one or more formed convex arcs; 
     a spline wheel disposed around the cam circumference, a plurality of spline apertures being arranged at an inner wall of the spline wheel; and 
     a bearing member disposed between the cam and the spline wheel, a plurality of bearing apertures being arranged at equal distance at a bearing member circumference, a roller being disposed at an active space of every bearing aperture, the cam driving the convex arc to rotate by an input force, the convex arc being powered to drive the roller to move into a corresponding spline aperture so as to actuate a rotational output at a specific reduction ratio generated by one of the spline wheel and the bearing member; 
     wherein, formation of the convex arc is restricted by the following equation:
 
 F×R sinθ&lt; R×μ×F cosθ
 
0&lt;θ≦4°
 
     wherein, F is a positive force for the roller pressing on the convex arc, R is a distance between a contact point of the convex arc and the roller and a cam axis, θ is a lead angle of the positive force F, μ is a relative friction coefficient between the convex arc and the roller. The lead angle means an angle formed by a tangent line of contact points between the rollers and the cam and a vertical line connected from the contact points to the cam axis. 
     According to the preferred embodiment of the present invention, in the following equation:
 
 F×R sinθ= T   1  
 
 R×μ×F cosθ= T   2  
 
     wherein, T 1  is a rotation torque exerting on the convex arc by the roller, T 2  is a rotation torque of a component force (μ×Fcosθ) for a friction force (μ×F) when the convex arc contacts the roller. 
     According to the present invention, the effect and advantages are the wave speed reducer has self-locking function. In particular, when one of the bearing member and the spline wheel used as an output end carries out reverse transmission to be used as an input end, self-locking function occurs between the cam, the roller, the bearing member and the spline member via the formation of the convex arc so as to protect transmission components in the reducer mechanism from unpredictable reverse rotation and from damages and danger. 
     According to the present invention, a method for designing a cam periphery comprising the following steps: 
     (A) slicing radial direction movement track of a roller between a cam and a spline aperture and circumference direction rotation track at equal proportion at equal time intervals to sequentially obtain circle centers and points of tangency of the track circles during movement of the roller; 
     (B) connecting the points of tangency to form a unit cam circumference segment of a cam periphery; and 
     (C) forming the cam periphery by mirroring and projecting the unit cam circumference segment respectively based on a X-coordinate and Y-coordinate from a cam axis. 
     According to the present invention, X-coordinates and Y-coordinates (X m , Y m ) of the circle centers of the track circles are obtained according to the following equation
 
[ X   m   ,Y   m ]=[( L   f   −M·Δy ′)·sin( M ·Δα),( L   f   −M·Δy ′)·cos( M ·Δα),]
 
wherein, L f  is a distance between a cam axis and a circle center of the track circle of a roller far away from the cam axis, M is an amount for equally dividing the single-sided tooth flank contour of the spline aperture, Δy′ is an equal divided amount of an effective radial displacement for each of the track circles of the roller, Δα is an equal amount of an effective rotational angle for each of the track circles of the roller.
 
     According to the present invention, X-coordinates and Y-coordinates (X′ m , Y′ m ) of the points of tangency of the track circles are obtained according to the following equation 
     
       
         
           
             
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     wherein, m is an integer representing a m th  track circle during movement of the roller, m is an integer larger than zero, R d  is a diameter of the roller, (X m-1 , Y m-1 ) is an X-coordinate and Y-coordinate (X m , Y m ) of the m th  circle center of the track circles. 
     According to the present invention, a method for designing a spline surface contour comprising the following steps: 
     (A) slicing radial direction movement track of a roller between a cam and a spline aperture and circumference direction rotation track at equal proportion at equal time intervals to sequentially obtain circle centers and points of tangency of the track circles during movement of the roller; 
     (B) connecting the points of tangency to form a single-sided tooth flank contour on spline aperture between a tooth crest and a void between the teeth; and 
     (C) forming a correspondent side tooth flank contour by mirroring the single-sided tooth flank contour based on a centerline of the void between the teeth in order to form the spline surface contour by connecting a void contour between the single-sided tooth flank contour and the correspondent side tooth flank contour. 
     According to the present invention, X-coordinates and Y-coordinates (X n , Y n ) of the circle centers of the track circles are obtained according to the following equation
 
[ X   n   ,Y   n ]=[( L   f   −N·Δy )·sin( N ·Δθ),( L   f   −N·Δy )·cos( N ·Δθ),]
 
     wherein, L f  is a distance between a cam axis and a circle center of the track circle of a roller far away from the cam axis, N is an amount for equally dividing the single-sided tooth flank contour of the spline aperture, Δy is an equal divided amount of an effective radial displacement for each of the track circles of the roller, Δθ is an equal divided amount of an effective rotational angle for each of the track circles of the roller. 
     According to the present invention, X-coordinates and Y-coordinates (X′ n , X′ n ) of the points of tangency of the track circles are obtained according to the following equation 
     
       
         
           
             
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     wherein, n−1 is an integer representing a n th  track circle during movement of the roller, n is an integer larger than zero, R d  is a diameter of the roller, (X n-1 , Y n-1 ) is an X-coordinate and Y-coordinate (X n , Y n ) of the n th  circle center of the track circles. 
     According to the present invention, a method for designing a spline wheel contour comprising the following steps: 
     applying the designing method of claim  1 ; and 
     based on a rotational center of the cam axis, arranging an array of internal cam faces around the spline wheel at equal circumference distance on the spline surface contour to form a spline wheel contour. 
     In order to achieve technical effects of the cam periphery, the spline surface contour and the spline wheel contour, under the condition of obtaining self-locking function of the wave speed reducer, the method can design a tooth flank contour in order to design a cam circumference segment of a spline wheel, and can design a cam periphery matched with the spline apertures in the spline wheel according to the ideal moving way of the rollers in the roller-type wave-motion so as to sufficiently and really transmit driving force exerted from the rollers via a tooth flank during a process of the cam surface pushing the rollers to contact tooth flank of the spline apertures. The tooth flank can be used as an effective contact surface of the cam for providing force to the rollers in order to maintain good driving accuracy and driving efficiency at a ratio of reduction of a certain output value for the roller-type wave-motion, and the driving accuracy at the output end of the roller-type wave-motion is increased. 
     In accordance with the implementation of the present invention, those skilled in the art can know that self-locking restraining conditions are not contradict and matched with the designing method of the cam periphery. 
     In accordance with one embodiment of the present invention, there is provided a compound type reducer device for applying to the wave speed reducer comprising a planetary gear set combined at one side of the wave speed reducer and a cam with a tooth ring at a cam inner surface, wherein the planetary gear set comprises a plurality of planetary gears disposed at a periphery surface of a wheel disk at its one side and spaced apart at equal distance and engaged with each of the tooth rings on the cam, the wheel disk is connected to a spin-wave driver by a shaft. The planetary gear set further comprises a sun gear through which the sun gear is connected to the spin-wave driver by a shaft, the plurality of planetary gears respectively are engaged with the sun gear for receiving transmission. 
     In accordance with one embodiment of the present invention, the plurality of planetary gears further comprises a periphery gear used as a fixing end and combined to a circumference of the plurality of planetary gears which comprises a plurality of gear sets, each of which comprises a front gear and a rear gear co-axially arranged, the front gears are engaged with the periphery gear and the plurality of planetary gears are respectively engaged with the tooth ring of the cam by the rear gears. Furthermore, a ring disk is formed and extends from a center of the bearing member to be used as an output shaft. The convex arc is used to drive the rollers because a component force generated by the rollers and the spline aperture drives the ring disk of the bearing member to output rotation force. 
     In accordance with another embodiment of the present invention, a compound type reducer device for applying to the wave speed reducer comprising a planetary gear set combined at one side of the wave speed reducer, wherein the planetary gear set comprises 
     a sun gear connected to a spin-wave driver by a shaft; and 
     a plurality of planetary gears disposed at a periphery surface of a cam at its one side and spaced apart at equal distance and respectively engaged with a periphery of the sun gear to drive and rotate the cam. 
     In accordance with another embodiment of the present invention, the plurality of planetary gears comprises: 
     a first set planetary gear comprising front gears disposed at a periphery surface of a wheel disk at its one side and spaced apart at equal distance, the plurality of planetary gears being combined and engaged with a periphery of the sun gear via the front gears, a center gear being disposed and fixed at a rotation center of the wheel disk at its another side; and 
     a second set planetary gear comprising rear gears disposed at a periphery surface of a cam at its one side and spaced apart at equal distance, the rear gears being combined and engaged with a periphery of the center gear. 
     wave speed in order to achieve the wave speed reduction function of the compound type wave speed reducer, the planetary gear set will generate the first stage of reduction effect, and the second stage wave reducer generates a second stage of wave speed reducing effects, the combination of the first and second stage of wave speed reduction will create a compound wave speed reduction effect. The first stage planetary wave speed reduction set can be designed with various wave speed reduction ratio in order to meet the demand of the users 
     Other objectives, advantages, and novel features of the invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an arrangement schematic diagram of a conventional worm shaft and a conventional worm wheel; 
         FIG. 2  is a schematic diagram showing a lead angle between the conventional worm shaft and worm wheel of  FIG. 1 ; 
         FIG. 3  is a three-dimensional explosive view of a wave speed reducer of the present invention; 
         FIG. 4  is a cross-section view of the wave speed reducer of  FIG. 3  of the present invention; 
         FIG. 4 a    illustrates an enlarged view of a cam, a roller and a spline aperture of  FIG. 4  of the present invention; 
         FIG. 5  illustrates a schematic diagram showing force balance between the cam, the roller and the spline aperture of  FIG. 4  of the present invention; 
         FIG. 6  is a schematic diagram showing a lead angle between the cam, the roller and the spline aperture of  FIG. 5  of the present invention; 
         FIG. 7  is a flowchart showing a process and steps for designing a spline surface contour according to the invention; 
         FIG. 8  is a cross-sectional view showing a spline surface contour and a cam periphery according to the invention; 
         FIG. 9  is an enlarged schematic diagram showing an effective movement range of track circles of rollers in the cam circumference according to the invention; 
         FIG. 10  is a flowchart showing a process of designing a spline surface contour according to the invention; 
         FIG. 11  is an enlarged schematic diagram showing an effective movement range of track circles of rollers in the spline aperture of  FIG. 8  according to the invention; 
         FIG. 12  is schematic diagram showing an equal amount dividend of the effective movement range of track circles of the rollers of  FIG. 11  according to the invention; 
         FIG. 13  is a flowchart showing a process of designing a spline wheel contour according to the invention; 
         FIG. 14  is a three-dimensional explosive view of a first embodiment of a compound type reducer device of the present invention; 
         FIG. 14 a    is a partial explosive view of another embodiment of a compound type reducer device of  FIG. 14  of the present invention; 
         FIGS. 15 and 16  are respectively three-dimensional explosive view of the compound type reducer device of  FIG. 14  viewed at different angles. 
         FIG. 17  is a cross-section view of the compound type reducer device of  FIG. 14  of the present invention; 
         FIG. 18  is a three-dimensional explosive view of a second embodiment of the compound type reducer device of the present invention. 
         FIG. 19  is a schematic diagram showing of the compound type reducer device of the present invention shown in  FIG. 18 . 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Please refer to  FIGS. 3 and 4  which respectively demonstrate the members and the arrangement of the wave speed reducer designed in the present invention. A cam  1 , a plurality of rollers  2 , a bearing member  4  and a spline wheel  3  are arranged co-axially from inside to outside between a seat  5  and a cover  6  in the wave speed reducer. An input shaft  14  is disposed at the axial position of the cam  1  to be used as an input end of the force of the wave speed reducer. The input shaft  14  can be transmitted rotational energy to input and drive the cam  1  to rotate. A convex arc  12  in spline line shape and located relatively far from the axis  11  is disposed in a cam surface  10  of the cam  1 . The convex arc  12  is used as an effective functional area for pushing and driving the roller to transmit power. A cam periphery  13  is formed on the cam  1 . In a preferred embodiment of the invention, the roller  2  is in cylinder shape. But, the roller  2  might be a bearing bead used as a roller part. The spline wheel  3  is in ring shape and is disposed co-axially at the outside of the cam surface  10  of the cam  1 . A plurality of spline apertures  30  are disposed at the inner wall of the spline wheel  3  so as to accommodate the roller  2  to be arranged between the cam surface  10  of the cam  1  and the spline apertures  30  of the spline wheel  3 . The bearing member  4  is disposed between the cam  1  and the spline wheel  3 . A plurality of bearing apertures  40  for accommodating the rollers  2  to rotate are disposed at equal distance of the circumference of the bearing member  4 . 
     Please refer to  FIG. 4 a    which shows an enlarged schematic diagram demonstrating the special relationship of the spline aperture  30 , the cam  1  and the roller  2 . In the preferred embodiment of the invention,  FIG. 4 a    demonstrates that the convex arc  12  of the cam surface  10  drives some rollers  2  to move into a relative location of the spline apertures  30  so as to contact the spline surface contour  31 , then, the bearing member  4  is driven by the transmitted driving force to generate an output rotation at a predetermined ratio of reduction. 
     For facilitating demonstration, in a preferred embodiment, the input shaft  14  the cam  1  is used as an input end and the spline wheel  3  is used to form an output shaft  41  at an axial position of the bearing member  4  as an output member. In a scope of the present invention, the bearing member  4  is included to demonstrate that the spline wheel  3  is used as an output end. Moreover, no matter the spline wheel  3  or the bearing member  4  is used as an output end, it will not affect the results showing the demonstration of the spline surface contour, the spline wheel contour and the cam periphery. 
     In the above example, the spline surface contour  31  comprises a single-sided tooth flank contour  31   a  and a correspondent side tooth flank contour  31   b  formed at a mirroring location of it. A void contour  33  is formed between the single-sided tooth flank contour  31   a  and the correspondent side tooth flank contour  31   b  to form a spline wheel contour  34  (as shown in  FIG. 4 ) by an array of the spline surface contour  31  to surround it. When the spline wheel contour  34  is formed, a single-side tooth flank contour  31   a  and a correspondent side tooth flank contour  31   b  of each spline surface contour  31  are respectively connected to a tooth crest contour  32  at a relatively far side to show the details of the spline wheel contour  34 . The said spline wheel contour  34  is referred to a specific contour of the inner wall of the spline wheel  3 . 
     In addition to the above details of the wave speed reducer of the present invention, in order to have self-locking function, in a force system in which force form the convex arc  12  is used and pushed to contact the rollers  2  so as to contact the bearing member  4  and the spline aperture  30 , a lead angle θ is designed. The details of the lead angle θ are explained as follows: 
     Please refer to  FIG. 5 . A cam  1  having a convex arc  12 , a roller  2 , a bearing member  4  and a spline aperture  30  shown in  FIG. 4  is disclosed to show state of a force system balance. When the cam  1  rotates counter-clockwise to drive, a function force F from the convex arc  12  is exerted on the roller  2  to press and contact so as to generate a component force F′ from the spline surface contour  31  relative to the roller  2 . A component force F″ from the bearing aperture  40  of the bearing member  4  is generated to exert on the roller  2 . At the same time, the three forces F, F′, F″ will generate state of a force system balance. 
     Please refer to  FIG. 6  which shows a schematic diagram in which when the convex arc  12  shown in  FIG. 5 b    presses and pushes the roller  2 , a contact point P is formed between the convex arc  12  and the roller  2 . A distance R from the contact point P and cam axis  11  is shown. From the principle of force and reaction force, it can be known that a positive force F originating from the roller  2  which exerts on the convex arc  12  at the contact point P is the same as the force F by which. A friction force u×F is formed at the contact point P, wherein μ is a relative friction coefficient between the convex arc and the roller. Because the shape of the convex arc  12  is not a real circular cam circumference segment in comparison with the axis  11  of the cam  1 , a angle θ is formed by crossing a function line along the positive force F at the contact point P with a connecting line of distance R from the contact point P to the cam axis  11 . In the present invention, the angle θ is defined as a lead angle θ. A friction component force μ×Fcosθ is formed and generated by dividing the friction force u×F with existence of the lead angle θ. 
     From  FIG. 6 , it can be known that near the rotation center  11  of the cam  1 , a function line r which is vertical to the positive force F is formed. By the equation r=Rsinθ and by the formation of the lead angle θ, when the roller  2  exerts the positive force F onto the convex arc  12 , it will generate a torque T 1  exerting from the rotation center  11  of the cam  1  with an equation of T 1 =F×r=F×Rsinθ. When the convex arc  12  contacts with the roller  2 , a friction force μ×F is generated. Thus, a friction component force μ×Fcosθ will form a torque T 2  onto the rotation center  11  of the cam  1  with an equation of T 2 =R×μ×Fcosθ. When T 1 &lt;T 2 , the wave speed reducer of the present invention can achieve self-locking effects. Therefore, when the convex arc  12  is designed in the present invention, the design must meet the requirements of the following equation (1)
 
 F×R sinθ&lt; R×μ×F cosθ
 
     After calculation of the above equation (1), the lead angle θ can be obtained through the following equation (2) 
     
       
         
           
             
               
                 sin 
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                 cos 
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                 ⁢ 
                 θ 
               
             
             = 
             
               
                 tan 
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                 θ 
               
               &lt; 
               
                 μ 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   
                     θ 
                     &lt; 
                     
                       
                         tan 
                         
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       μ 
                     
                   
                   ) 
                 
               
             
           
         
       
     
     According to the equation (2), the convex arc  12 , the roller  2 , the bearing member  4  and the spline aperture  30  of the cam  1  are made of steel. A relative friction coefficient μ between a first steel material and a second steel mater is between 0.1˜0.12 obtained from a material table. The present invention assumes the relative friction coefficient between the convex arc  12  and the roller 2μ=0.07 and enters it into the equation (2) to get the lead angle θ&lt;4′. It can be known that the resulting relative friction coefficient between the convex arc  12  and the roller 2μ=0.07 is smaller than the values of 0.1˜0.12 obtained from the material table. Thus, when 0&lt;θ≦4°, it can achieve the self-locking effect. 
     The self-locking effect means when the bearing member  4  (or it is replaced by the spline wheel  3 ) used as an output end reversely transits as an input end of the cam  1 , it is restricted by the equation (1) to limit the lead angle into a range of 0&lt;θ≦4°, the self-locking effect occurs between the cam  1 , roller  2 , bearing member  4  and the spline wheel  3  so as to protect the transmission components of the reducer mechanism from un-predictable reverse rotation and damages and rick (will explain later). 
     In order to meet the requirements of the lead angle θ, the present invention provide a preferred design plan regarding the spline surface contour  31  comprising steps of S 1  to S 5  (as shown in  FIG. 7 ). 
     Step S 1 : designing a movement track of a roller; 
     Before the arrangement of cam periphery  13  and spline surface contour  31  is known, the movement track of the roller  2  is analyzed firstly. In more details, when the convex arc  12  of the cam surface  10  contacts the roller  2  to gradually push to generate two kinds of movement velocities in the spline aperture  30 . The two movement velocities include a radial movement velocity v in the radial direction of the cam axis  11  and an angular velocity w in the rotational direction relative to the circumference of the cam  1  (as shown in  FIG. 4 a   ). A radial displacement amount L is equally divided by an unit time t to get a radial displacement velocity v (ΔL=v×Δt). The unit time t is used to divide an effective rotation angular θ in the circumference direction to get an angular velocity ω (Δθ=ω×Δt) so as to obtaining and simulating movement tracks of the roller  2  in spline aperture  30  and to draw track circles (as shown in steps  2  to  4 ). 
     step S 2 : initially setting up. 
     In order to meet the requirements of good ratio of reduction and arrangement dimensional size,  FIG. 8  can be drawn by the following data and steps in the following examples.  FIG. 8  is demonstrated to show a figure in four quadrants of X-Y coordinate system, especially to show a figure of track circles of the roller  2  in the second quadrant by using the set parameters. The set-up parameters are as follows: 
     1. a set amount R n  of the rollers R n =40. In order to make sure that the rigidity of the bearing apertures  40  is excellent, the actual amount of the rollers and bearing apertures is a half of R n . 
     2. a set amount C n  of the convex arcs of the cam  1  C n =2. 
     3. an amount of the spline apertures S n =R n −C n =40−2=38. 
     4. a roller diameter R d =2.0 mm. 
     5. an effective function amount E n  of the rollers is non-integer number, for example E n =5.3. 
     step S 3 : drawing track circles of the rollers in the spline apertures. 
     According to set arrangement of step  2 , a figure of an effective movement range of the roller track circles is drawn as shown in  FIG. 9  based on the following parameters and definition. 
     After the status of  FIG. 9 , an appropriate equal amount M for the effective movement range (including the effective radial displacement amount δy and the effective circumference displacement angle δθ) is drawn and divided. The equal amount M is used as an equal amount for dividing the cam periphery  13 . A proportionally equal amount of effective radial displacement divided by the equal amount M (e.g. M=300) for a radial displacement Δy′ of each track circle is as follows: 
               Δ   ⁢           ⁢     y   ′       =         δ   ⁢           ⁢   y     M     =       0.52   300     =     0.0017333   ⁢           ⁢     mm   .                 
The arc lines generated are numbered from outside to inside as L′ 0 , L′ 1 , L′ 2 , . . . L′ M  (M=300). The rotational angle Δα of each roller track circle for an effective rotational angle obtained by divided using an predetermined equal amount of M is as follows:
 
             Δα   =       δα   M     =       38.7   300     =     0.129   ⁢     °   .                 
The radiation lines generated are numbered from left to right as A′ 0 , A′ 1 , A′ 2 , . . . , A′ M  (M=300).
 
     Thus, each intersection point intersected by the arc lines L′ 0 , L′ 1 , L′ 2 , . . . , L′ M  and the radiation lines A′ 0 , A′ 1 , A′ 2 , . . . , A′ M  are used as circle centers of the roller track circles to sequentially draw track circles (roller diameter R d =2.0 mm) The margin between the roller  2  and the cam surface  10  is considered. For example, a pre-determined margin for a roller diameter R d +=2.0+0.04=2.04 mm. The X, Y-coordinates (X m , Y m ) of the circle centers of the track circles are obtained as the following equation (3)
 
[ X   m   ,Y   m ]=[( L   f   −M·Δy ′)·sin( M ·Δα),( L   f   −M·Δy ′)·cos( M ·Δα),]
 
     From the above descriptions, the coordinates of the 0 th  circle center is [X 0 , Y 0 ]=[0, L f ]=[0,14.6]. The coordinates of the 2 th  circle center is [X 1 , Y 1 ]=[−0.032868, 14.598230]. It can be inferred that the coordinates of the (m+1) th  circle center is [X m , Y m ]=[−8.8034166, 10.988460] (when m=M=300 equally divided). 
     step S 4 : drawing a unit cam circumference segment of the cam. 
     After the above step S 3 , a tangent T′ is formed to connect two neighboring track circles. A 1 th  circle point of tangency for each T′ is selected and coordinates [X′ m , Y′ m ] of each circle point of tangency are calculated by the following equation (4) 
     
       
         
           
             
               { 
               
                 
                   X 
                   m 
                   ′ 
                 
                 , 
                 
                   Y 
                   m 
                   ′ 
                 
               
               } 
             
             = 
             
               { 
               
                 
                   
                     X 
                     m 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           R 
                           d 
                         
                         2 
                       
                       ) 
                     
                     · 
                     
                       sin 
                       ⁡ 
                       
                         [ 
                         
                           
                             tan 
                             
                               - 
                               1 
                             
                           
                           | 
                           
                             
                               ( 
                               
                                 
                                   Y 
                                   m 
                                 
                                 - 
                                 
                                   Y 
                                   
                                     m 
                                     - 
                                     1 
                                   
                                 
                               
                               ) 
                             
                             
                               ( 
                               
                                 
                                   X 
                                   m 
                                 
                                 - 
                                 
                                   X 
                                   
                                     m 
                                     - 
                                     1 
                                   
                                 
                               
                               ) 
                             
                           
                           | 
                         
                         ] 
                       
                     
                   
                 
                 , 
                 
                   
                     Y 
                     m 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           R 
                           d 
                         
                         2 
                       
                       ) 
                     
                     · 
                     
                       cos 
                       ⁡ 
                       
                         [ 
                         
                           
                             tan 
                             
                               - 
                               1 
                             
                           
                           | 
                           
                             
                               ( 
                               
                                 
                                   Y 
                                   m 
                                 
                                 - 
                                 
                                   Y 
                                   
                                     m 
                                     - 
                                     1 
                                   
                                 
                               
                               ) 
                             
                             
                               ( 
                               
                                 
                                   X 
                                   m 
                                 
                                 - 
                                 
                                   X 
                                   
                                     m 
                                     - 
                                     1 
                                   
                                 
                               
                               ) 
                             
                           
                           | 
                         
                         ] 
                       
                     
                   
                 
               
               } 
             
           
         
       
     
     wherein, X m-1 , Y m-1  are coordinates of the circle center of the m th  track circle. 
     From the above descriptions, point of tangency coordinates [X′ 0 , Y′ 0 ]=[0.053785, 13.601447] of a 1 th  track circle, point of tangency coordinates [X′ 1 , Y′ 1 ]=[0.023171, 13.599801] of a 2 th  track circle are sequentially obtained. It can be inferred that point of tangency coordinates [X′ m , Y′ m ]=[−8.135657, 10.244083] of a (m+1) th  track circle (when m=M=300 as equal amount for dividing) are obtained. The points of tangency in the second quadrant are connected by using spline lines to form a single body, i.e. to form unit cam circumference segment  13   a  in the cam periphery  13 . The points of tangency covered and connected by tangent T′ are the spline line contour location of the partial convex arc  12  of the cam  1  in the second quadrant. A range of the unit cam circumference segment  13   a  formed and connected by the spline lines includes the spline line contour of the partial convex arc  12  and the cam surface of the part other than convex arc  12 . 
     step S 5 : drawing cam periphery. 
     Please refer to  FIGS. 4 and 9  which is a schematic diagram showing a unit cam circumference segment  13   a  (as shown in  FIG. 9 ) formed in the 2 th  quadrant drawn in step S 40 . Based on a cam axis  11 , the cam periphery  13  is respectively mirrored and projected to the 1th, 3th and 4 th  quadrants across the X-coordinate and Y-coordinate. The so-called “respectively mirrored and projected” includes a mirroring projection across the X-coordinate and then a mirroring projection across the Y-coordinate, or a mirroring projection across the Y-coordinate and then a mirroring projection across the X-coordinate so as to form images of the unit cam circumference segment  13   a  in any of the four quadrants. In order to sequentially mirror and project the image onto the other three quadrants and to project the images onto the all four quadrants of X-Y coordinate system, a whole drawing of cam periphery  13  (as shown in  FIG. 4 ) is formed by surrounding around. The extra lines and tips of the unit cam circumference segment  13   a  generated at an intersection point on the Y-coordinate can be revised in round angle way or in small arc way. 
     The word “effective” in the above descriptions means to be effective at angle range when the roller  2 , the spline wheel  3 , the cam  1  and the bearing member  4  simultaneously contact. Out of the angle range, the word “effective” should be “ineffective”. The limiting condition (equation (1)) of the lead angle should be incorporated and implemented in a process that the convex arc  12  can effectively contact and push the roller  2  to move in an angle range. 
     Furthermore, the present invention can provide a method of designing a spline surface contour  31 , more specific, it comprises steps of executing steps S 30  to Step  50  (shown in  FIG. 10 ) after the steps of Step S 1  to step S 2 . 
     step S 30 : drawing track circles of the rollers in the spline apertures. 
     According to set-up arrangement of step  2 , a figure of an effective movement range of the roller track circles is drawn as shown in  FIG. 11  (matched with  FIG. 8 ) based on the following parameters and definition of the above example: 
     6. a distance L f  between a circle center of a roller track circles of farest cam axis  11  and the cam axis  11 , predetermined coordinates (0, L f ), wherein L f =14.6 mm. 
     7. a tangent angle between two initially set-up track circles in the example: 44.5°˜45.5°. 
     8. an effective radial displacement of the roller: 0.52 mm. 
     9. an effective circumference angle of the roller δα, 
             δα   =         360     R   n       ×     (       E   n     -   1     )       =         360   40     ×     (     5.3   -   1     )       =     38.7   ⁢   °               
(as shown in  FIG. 3 ).
 
     10. from the above descriptions, a relative angular difference Δβ between the spline aperture and the roller is calculated: 
     
       
         
           
             Δβ 
             = 
             
               
                 
                   360 
                   
                     R 
                     n 
                   
                 
                 - 
                 
                   360 
                   
                     S 
                     n 
                   
                 
               
               = 
               
                 
                   
                     360 
                     38 
                   
                   - 
                   
                     360 
                     40 
                   
                 
                 = 
                 
                   0.47368 
                   ⁢ 
                   
                     
                       ° 
                       ⁡ 
                       
                         ( 
                         
                           not 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           shown 
                         
                         ) 
                       
                     
                     . 
                   
                 
               
             
           
         
       
     
     11. a displacement angle δθ of an effective function range of the single-sided tooth flank contour  31   a  of the set-up spline aperture  30 , i.e. 
     
       
         
           
             δθ 
             = 
             
               
                 
                   ( 
                   
                     
                       360 
                       
                         R 
                         n 
                       
                     
                     - 
                     
                       360 
                       
                         S 
                         n 
                       
                     
                   
                   ) 
                 
                 × 
                 
                   ( 
                   
                     
                       E 
                       n 
                     
                     - 
                     1 
                   
                   ) 
                 
               
               = 
               
                 
                   
                     ( 
                     
                       
                         360 
                         38 
                       
                       - 
                       
                         360 
                         40 
                       
                     
                     ) 
                   
                   × 
                   
                     ( 
                     
                       5.3 
                       - 
                       1 
                     
                     ) 
                   
                 
                 = 
                 
                   2.0368 
                   ⁢ 
                   
                     ° 
                     . 
                   
                 
               
             
           
         
       
     
     After the status of  FIG. 11 , an appropriate equal amount N for the effective movement range (including the effective radial displacement amount δy and the effective circumference displacement angle δθ) is drawn and divided. The equal amount N is used as an equal amount for dividing the single-sided tooth flank contour  31   a  of the spline aperture as shown in  FIG. 6 . A proportionally equal amount of effective radial displacement divided by the equal amount N (e.g. N=100) for a radial displacement Δy of each track circle is as follows: 
     
       
         
           
             
               Δ 
               ⁢ 
               
                   
               
               ⁢ 
               y 
             
             = 
             
               
                 
                   δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   y 
                 
                 N 
               
               = 
               
                 
                   0.52 
                   100 
                 
                 = 
                 
                   0.0052 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     mm 
                     . 
                   
                 
               
             
           
         
       
     
     The arc lines generated are numbered from outside to inside as L 0 , L 1 , L 2 , . . . L N . The rotational angle Δθ of each roller track circle for an effective rotational angle obtained by divided using an predetermined equal amount of N is as follows: 
             Δθ   =       δθ   N     =       2.0368   100     =     0.02038   ⁢     °   .                 
The radiation lines generated are numbered from left to right as A 0 , A 1 , A 2 , . . . , A N .
 
     Thus, each intersection point intersected by the arc lines L 0 , L 1 , L 2 , . . . L N  and the radiation lines A 0 , A 1 , A 2 , . . . , A N  are used as circle centers of the roller track circles to sequentially draw track circles (roller diameter R d =2.0 mm) The X, Y-coordinates (X n , Y n ) of the circle centers of the track circles are obtained as the following equation (5)
 
[ X   n   ,Y   n ]=[( L   f   −N·Δy )·sin( N ·Δθ),( L   f   −N·Δy )·cos( N ·Δθ),]
 
     Wherein, n represents a numbering integer of the track circles for each roller. n is an integer larger than zero. 
     From the above descriptions, the coordinates of the 0 th  circle center is [X 0 , Y 0 ]=[0, L f ]=[0,14.6]. The coordinates of the 1 th  circle center is [X 1 , Y 1  ]=[0.005188, 14.594799]. It can be inferred that the coordinates of the (n+1) th  circle center is [X n , Y n ]=[0.500433, 14.071104] (when n=N=100 equally divided). 
     step S 4 : drawing a unit cam circumference segment of the cam. 
     After the above step S 30 , a tangent T is formed to connect two neighboring track circles. A 1 th  circle point of tangency for each T is selected and coordinates [X′ n , X′ n ] of each circle points of tangency are calculated by the following equation (2) 
     
       
         
           
             
               { 
               
                 
                   X 
                   n 
                   ′ 
                 
                 , 
                 
                   Y 
                   n 
                   ′ 
                 
               
               } 
             
             = 
             
               { 
               
                 
                   
                     X 
                     n 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           R 
                           d 
                         
                         2 
                       
                       ) 
                     
                     · 
                     
                       sin 
                       ⁡ 
                       
                         [ 
                         
                           
                             tan 
                             
                               - 
                               1 
                             
                           
                           | 
                           
                             
                               ( 
                               
                                 
                                   Y 
                                   n 
                                 
                                 - 
                                 
                                   Y 
                                   
                                     n 
                                     - 
                                     1 
                                   
                                 
                               
                               ) 
                             
                             
                               ( 
                               
                                 
                                   X 
                                   n 
                                 
                                 - 
                                 
                                   X 
                                   
                                     n 
                                     - 
                                     1 
                                   
                                 
                               
                               ) 
                             
                           
                           | 
                         
                         ] 
                       
                     
                   
                 
                 , 
                 
                   
                     Y 
                     n 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           R 
                           d 
                         
                         2 
                       
                       ) 
                     
                     · 
                     
                       cos 
                       ⁡ 
                       
                         [ 
                         
                           
                             tan 
                             
                               - 
                               1 
                             
                           
                           | 
                           
                             
                               ( 
                               
                                 
                                   Y 
                                   n 
                                 
                                 - 
                                 
                                   Y 
                                   
                                     n 
                                     - 
                                     1 
                                   
                                 
                               
                               ) 
                             
                             
                               ( 
                               
                                 
                                   X 
                                   n 
                                 
                                 - 
                                 
                                   X 
                                   
                                     n 
                                     - 
                                     1 
                                   
                                 
                               
                               ) 
                             
                           
                           | 
                         
                         ] 
                       
                     
                   
                 
               
               } 
             
           
         
       
     
     wherein, X n-1 , Y n-1  are coordinates of the circle center of the n th  track circle. 
     From the above descriptions, point of tangency coordinates [X′ 0 , Y′ 0 ]=[0.707959, 15.306254] of a 1 th  track circle, point of tangency coordinates [X′ 1 , Y′ 1 ]=[0.713524, 15.300675] of a 2 th  track circle are sequentially obtained. It can be inferred that point of tangency coordinates [X′ n , Y′ n ]=[1.245266, 14.738354] of a (n+1) th  track circle (when n=N=100 as equal amount for dividing) are obtained. 
     Spline lines are used to connect the points of tangency of the circles to form a surface body. The single-sided tooth flank contour  31   a  between the tooth crest and tooth void is formed on the spline aperture  30 . It should be noted that the tooth crest and the tooth void are the so-called predetermined space which is virtual having no real contour lines. Those skilled in the art can understand that a tooth crest and a tooth void are formed at both ends of the spline aperture tooth flank. According to the step S 2 , from the parameters, such as the amount S n  of the spline apertures, the amount R n  of the rollers and roller diameter R d , the distance between the tooth crest and the tooth void on the spline wheel can be known for facilitating formation of single sided tooth flank contour  31   a  and the contour of the tooth crest and the tooth void after the correspondent side tooth flank contour  31   b  is formed. 
     step S 50 : drawing spline surface contour. 
     After step S 40 , please refer to  FIG. 4 , a centerline Y (actually is a connecting line between a circle center of the 0 th  track circle and the cam axis  11  in  FIG. 6 ) of virtual tooth void is used to mirror an image of the single-sided tooth flank contour  31   a  to form the correspondent side tooth flank contour  31   b.    
     Circle points of tangency of two neighboring track circles between the single-sided tooth flank contour  31   a  and the correspondent side tooth flank contour  31   b  are connected and a real tooth void contour  33  which does not interfere with the circle surface of the track circles is formed at the tooth void location, then, e.g. contour lines of convex or arc shape are formed. The spline surface contour  31  is formed by connecting the void contour  33  between the single-sided tooth flank contour  31   a  and the correspondent side tooth flank contour  31   b . The virtual tooth crest portion is drawn after the whole spline wheel contour  34  is form. 
     Another embodiment of the invention is to implement drawing a spline wheel contour  34 . In more details, the embodiment comprises the step S 50  of drawing spline surface contour  31  and implementing the following step S 60  (as shown in  FIG. 13 ). 
     Step S 60 : drawing the spline wheel contour. 
     After the step S 50 , the cam axis  11  is used as a rotational center (as shown in  FIG. 9 ), and an array spaced away at equal distance on the circumference of spline surface contour  31  having predetermined amount S n  of spline apertures surrounds around an inner surface of the spline wheel  3  to form the spline wheel contour  34 . The so-called equal space on the circumference means a distance formed by the predetermined virtual tooth crests. 
     In more details, the tooth crest portion is drawn to form a real tooth crest contour  32  (as shown in  FIG. 4 ) comprising tips far from the single-sided tooth flank contour  31   a  and the correspondent side tooth flank contour  31   b  for each spline surface contour  31  are connected in an arc. The meaning of “tips relatively far from are connected in round angle way” is that circle points of tangency of two correspondent track circles at the farest location between the single-sided tooth flank contour  31   a  and the correspondent side tooth flank contour  31   b  for each spline surface contour  31  are connected linearly in an arc so as to form an arrangement completely exhibiting the spline wheel contour  34  connecting the tooth crest contours  32  between the spline surface contours  31 . The tooth crest contour  32  is used for guiding the roller  2  to move into the adjacent spline aperture  30  to contact the spline surface contour  31 . The roller guiding includes a continuous contact-type guidance or non-continuous contact-type guidance or non-contact-type guidance. 
     The formation technique of forming the cam periphery  13 , the spline surface contour  31  and the spline wheel contour  34 , the wave speed reducer has self-locking function. When the cam periphery  10  pushes the roller  2  to contact the tooth-flank contours  31   a ,  31   b  of spline wheel  3 , the driving force fully really exerted from the roller  2  by using the tooth flanks. The tooth flanks is capable of providing effective contact surface generating a component force by the roller  2  onto the cam  1  in order to further providing increasing driving accuracy at the output end of the wave speed reducer when the wave speed reducer maintains its driving accuracy and driving efficiency of its output end at a reduction ratio. 
     Please refer to  FIGS. 14 to 17  which respectively disclose structural arrangement details of the preferred embodiments of the compound type reducer device of the present invention by applying and combining the above wave speed reducer. As a whole, the example includes a plurality of planetary gear set  800  combined to one side of the wave speed reducer. 
     In the example, the main components, their structural arrangement and configuration of the wave speed reducer of  FIG. 3  are slightly different from those of this example. The conditions, formation techniques and structural arrangement of the wave speed reducer disclosed in  FIGS. 4 to 13  are fundamentally the same as those of the example. 
     Please refer to  FIG. 14 . The members and the arrangement of the wave speed reducer designed in the example are the same. A cam  100 , a plurality of rollers  200 , a bearing member  400  and a spline wheel  300  are arranged co-axially from inside to outside between a seat  50  and a cover  60  in the wave speed reducer. The cam  100  is used as the input end in the example. The bearing member  400  is used as the output end by fixing to the spline wheel  300 . 
     As shown in  FIG. 14 , the main differences between  FIG. 14  and the  FIG. 3  are that in part  50  within the planetary gear set  800 , there is an internal gear structure  88 . Also input cam  100  which provide power input into the second stage of the speed reduction has no input shaft, it is replaced with internal gear  110  structure,  110  and  100  also share the same axis of rotation in order to provide an interface between power input and output. The rest of the structure is basically the same between  FIG. 14  and  FIG. 3   
     As shown in  FIG. 14 , the planetary gear set  800  includes a sun gear  800  and multiple planetary gears  820 . The combining view of  FIG. 14 ,  FIG. 15  and  FIG. 17  reveals that sun gear  810  is connected to an actuator  90 , the actuator  90  can be selected from a variety of motors which can provide the required level of input to drive the sun gear  810 , for example, a servo motor or a stepper motor can be used. The planetary gear carrier  85  has an opening in the center for the sun gear  810  to pass through in order to create gear meshing between sun gear  810  and planetary gears  820 . 
     From  FIGS. 15 and 17 , it can be known the plurality of planetary gears  820  are respectively engaged with a periphery of the sun gear  810 . The plurality of planetary gears  820  are respectively engaged with the tooth ring  110  at an inner periphery location of the cam  100 . The periphery gear  88  is engaged with a periphery of the plurality of planetary gears  820 . 
     From  FIGS. 15 and 17 , it can be known that the plurality of planetary gears  820  maybe comprises a plurality of gear sets  82  in implementation. Each gear set  82  comprises a front gear  82   a  and a rear gear  82   b  co-axially arranged. The front gears  82   a  are engaged with the periphery gear  88 . Because the periphery gear  88  is formed and fixed to the seat  50 , the periphery gear  88  can provide guidance and supporting for the front gear  82   a  so as to stably drive the front gears  82   a  by the sun gear  810  and to surround and rotate around the sun gear  810  and the periphery gear  88 . A first stage output rotation at a reduction ratio is formed. A second stage output rotation at a reduction ratio is formed after the rotation process the tooth ring  110  of the cam  100  is engaged with the rear gears  82   b  co-axially arranged together with the front gears  82   a . Thus, by using the wave speed reducer shown in the examples, the cam  100  outputting a rotation force at a second stage reduction ratio can drive parts of the rollers  200  to relatively move into the spline apertures  310  to contact with the spline surface contour in order to transmit driving power of a third stage reduction ratio to drive the bearing member  400  to rotate. 
     Those skilled in the art will easily know that output at multi-reduction ratio respectively through the planetary gear  800  and the wave speed reducer can be generated for a compound arrangement of the planetary gear  800  and the wave speed reducer to meet the requirements and needs at the output end. 
     In the example of  FIGS. 14 to 17 , in order to meet the requirements of different reduction ratios provided by the planetary gear set  800 , the sun gear  810  can be omitted. It is implemented in  FIG. 14 a    which demonstrate the planetary gear set does not include a sun gear and no holes for allowing passage of the sun gear are arranged at a disk center of the wheel disk  85 . Alternatively, a shaft hole is arranged at the disk center of the wheel disk  85  and connected to a center axis of the spin-wave driver  90 . In the implementation, a reduction ratio generated after no sun gear drives the plurality of planetary gears  820  will be omitted. The alternative reduction ratio can be obtained after the spin-wave driver  90  directly drives the plurality of planetary gears  820  and the cam  100  is driven. 
     In the example of  FIGS. 14 to 17 , a ring disk  410  is formed by extend from a center of the bearing member  400 . The ring disk  410  is used in the similar way as the output shaft  41  does in  FIG. 4  in order to connect the ring disk  410  to the outside to connect to the driving objects (for example, a mechanical arm). 
     Please refer to  FIGS. 18 and 19  which disclose another embodiment of multi-reduction ratio output of the compound type reducer device of the present invention.  FIGS. 18 and 19  differ from  FIGS. 14 to 17  in that the planetary gears  84  of the planetary gear set  840  are disposed at equal distance at edge circumference of the cam  101  and engaged with periphery of the sun gear  811 . In more details, The planetary gears  84  can be divided into a first set planetary gear  841  and a second set planetary gear  842 . The first set planetary gear  841  comprises front gears  841   a  which are disposed at equal distance at edge circumference of the wheel disk  841   b  and a center gear  841   c  which are disposed at equal distance at edge circumference of the wheel disk  841   b . The second set planetary gear  842  comprises rear gears  842   a  which are disposed at equal distance at edge circumference of the cam  101  and engaged with periphery of the center gear  841   c  in order to be used as a power input interface of the cam  101  for the rear gears  842   a . The front gears  841   a  are engaged with the periphery gear  880  located at the seat  500  used as a fixing end. Alternatively, no tooth rings can be disposed on the cam  101  to be a solid body. In addition to the above differences, the structure of this example is the same as that in the above examples. 
     According to the structural configuration, the spin-wave driver  91  which is connected to the sun gear  811  by a shaft is engaged with the front gears  841   a  to rotate around the periphery gear  880 , and a first stage reduction ratio output driving is generated through the driving of the wheel disk  841   b  and the center gear  841   c . A second stage reduction ratio output driving is generated after the center gear  841   c  is engaged with the rear gears  842   a  and the cam  101  to rotate. Thus, the cam  101  drives parts of the roller  201  to move into the corresponding spline aperture  311  to contact with the spline surface contour in order to transmit a third stage reduction ratio output driving to drive the bearing  401  to output and rotate. In this implementation, a multi-stage reduction ratio output driving is generated. 
     In conclusion, in the present invention a server motor can be used as a spin-wave driver and a loading object, such as, a mechanical arm, is connected to its output end. The mechanical arm can move in accurate tiny angle range by the multi-stage reduction ratio output driving, the excellent driving accuracy and the self-locking function. From the common knowledge, it could be known that a driver, such as, a server motor, is shut down by cutting off power and loses driving power and the center shaft of the motor will become a free end not to be maintained. A reverse direction torque against the output rotation direction of the mechanical arm because of its load is formed to exert on the compound type reducer device. According to the self-locking design of the present invention, a self-locking function is generated between the cam, the roller, the bearing member and the spline aperture by using the convex arc design of the cam. That is to say, reverse direction brake against the output rotation is generated to protect the mechanical arm at the output end from dropping and damages of the work components and to protect the transmission components of the compound type reducer device from the resulting un-predictable reverse rotation and damages and risk. 
     Although the present invention has been explained in relation to its preferred embodiment, it is to be understood that any other possible modifications and variations can be made without departing from the scope of the invention as hereinafter claimed.