WO2003083296A1 - Groupe de roue dynamique a moment variable - Google Patents

Groupe de roue dynamique a moment variable Download PDF

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Publication number
WO2003083296A1
WO2003083296A1 PCT/CN2003/000155 CN0300155W WO03083296A1 WO 2003083296 A1 WO2003083296 A1 WO 2003083296A1 CN 0300155 W CN0300155 W CN 0300155W WO 03083296 A1 WO03083296 A1 WO 03083296A1
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WO
WIPO (PCT)
Prior art keywords
wheel
force
weight
boom
torque
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Application number
PCT/CN2003/000155
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English (en)
French (fr)
Inventor
Zhaoyuan Li
Original Assignee
Zhaoyuan Li
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Publication date
Application filed by Zhaoyuan Li filed Critical Zhaoyuan Li
Priority to AU2003213344A priority Critical patent/AU2003213344A1/en
Publication of WO2003083296A1 publication Critical patent/WO2003083296A1/zh

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Classifications

    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03G—SPRING, WEIGHT, INERTIA OR LIKE MOTORS; MECHANICAL-POWER PRODUCING DEVICES OR MECHANISMS, NOT OTHERWISE PROVIDED FOR OR USING ENERGY SOURCES NOT OTHERWISE PROVIDED FOR
    • F03G7/00—Mechanical-power-producing mechanisms, not otherwise provided for or using energy sources not otherwise provided for
    • F03G7/10—Alleged perpetua mobilia
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03G—SPRING, WEIGHT, INERTIA OR LIKE MOTORS; MECHANICAL-POWER PRODUCING DEVICES OR MECHANISMS, NOT OTHERWISE PROVIDED FOR OR USING ENERGY SOURCES NOT OTHERWISE PROVIDED FOR
    • F03G7/00—Mechanical-power-producing mechanisms, not otherwise provided for or using energy sources not otherwise provided for
    • F03G7/10—Alleged perpetua mobilia
    • F03G7/104—Alleged perpetua mobilia continuously converting gravity into usable power
    • F03G7/107—Alleged perpetua mobilia continuously converting gravity into usable power using an unbalance for increasing torque or saving energy
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03G—SPRING, WEIGHT, INERTIA OR LIKE MOTORS; MECHANICAL-POWER PRODUCING DEVICES OR MECHANISMS, NOT OTHERWISE PROVIDED FOR OR USING ENERGY SOURCES NOT OTHERWISE PROVIDED FOR
    • F03G3/00—Other motors, e.g. gravity or inertia motors
    • F03G3/06—Other motors, e.g. gravity or inertia motors using pendulums
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03G—SPRING, WEIGHT, INERTIA OR LIKE MOTORS; MECHANICAL-POWER PRODUCING DEVICES OR MECHANISMS, NOT OTHERWISE PROVIDED FOR OR USING ENERGY SOURCES NOT OTHERWISE PROVIDED FOR
    • F03G3/00—Other motors, e.g. gravity or inertia motors
    • F03G3/08—Other motors, e.g. gravity or inertia motors using flywheels

Definitions

  • the present invention relates to a torque differential wheel set (refer to FIG. 2), referred to as a force differential wheel set, in particular to a power machine that applies the basic principles of physics to a lever combination machine and converts energy forms.
  • Force differential wheels (see Figure 3, Figure 4 is the reverse view of Figure 3) is a collection of several coaxial levers, and is also the basic unit constituting a force differential wheel set, each force differential wheel is horizontally penetrated by two through one shaft
  • An inscribed regular polygonal structure with a radius R is formed, and the two regular polygonal structures are fixed on the rotating shaft with an axial distance that is slightly larger than the length L of the weight; a plurality of radiuses R / 2, length L, and a density of D, a cylinder whose axial direction of the cylinder is parallel to the rotation axis of the force differential wheel, that is, the shaft protruding from both ends of the weight is lifted by a boom length R in the radial direction of the cylinder, and the other ends of the boom are respectively Equidistantly hanging on two equal vertices of two regular polygonal structures, the upper end of the boom horizontally penetrates the shaft by one of the fixed fan-shaped toothed wheels The end is called the boom tooth support wheel 12, which
  • the sector gear that is fixed and does not rotate constitutes an external gear set of + r ⁇ R.
  • the boom tooth wheel can rotate freely.
  • the support wheel it needs to be connected to a fixed sector wheel with a radius r 3 of the fixed sector wheel.
  • the invention is a power machine that applies the basic principles of physics to a lever combination machine and converts the energy form.
  • the feature of the invention is to use the force obtained by the weight or volume factor of the object (applicable to buoyancy in water) as the lever combination.
  • Shift see Figure 1
  • the moment arm can be changed accordingly, and using the principle of the bar and pestle, the object that originally did negative work is moved to the place where positive work is performed.
  • the rotational power converted from the universal gravitation by the force differential wheel set is also an inexhaustible and inexhaustible source of energy.
  • the force differential wheel set uses the universal gravitational moment as its source of power. No other fuel is needed. Therefore, the force differential wheel set is suitable for any environment and will not pollute the environment.
  • FIG. 1 Schematic diagram of zero moment line offset
  • FIG. 1 Perspective view of the torque difference moving wheel set
  • Figure 3 Front view, side view, top view of the differential force wheel
  • Figure 7 Schematic diagram of boom, weight, and round wheel assembly
  • Figure 11 Action diagram of boom tooth support wheel and fixed fan tooth wheel
  • the fixed sector toothed round (see Figure 6) is a small sector gear with two radii and rim structures that are not the same. They are concentrically connected to form a larger sector toothed round and are fixed to the difference in torque. On each bracket of the wheel set. Fixed sector toothed rounds, including fixed sector gears with smaller center angles and a pitch circle radius of r 2 at one end of the larger sector toothed round (the side close to the hanging weight point) and a larger sector toothed circle The other end of the wheel is a fixed sector circular wheel with a large center angle and a radius r 3 .
  • the fixed sector wheel with a large center angle is based on the fixed sector gear, starting from the fixed sector gear end (the side separated from the boom tooth support), with the same center as the center and r 3 as the radius In the direction of the rotation of the force difference wheel, the center angle is widened, and no object is set on the field around the radius r 3 .
  • the starting edge of the fan-shaped round coincides with the end of the fixed fan-shaped gear, the fan-shaped areas do not overlap, and they are all fixed in the same plane.
  • the ground velocity is also zero.
  • the distance between the two points in the longitudinal axis is R, the end connected to the regular polygon is the upper end, and the end connected to the weight is the lower end.
  • the upper shaft must overlap the hanging weight point of the force difference wheel, and a horizontal axis passing through the two points and parallel to the rotation axis of the force difference wheel, and integrated with the boom, so that the boom can be centered on this axis , Rotating in a plane perpendicular to the axial direction of the weight; the cylindrical axis protruding at either end of the weight passes through the bearing at the lower end and lifting the same weight in the same way with the other boom at the other end of the weight Hammer (see Figure 7).
  • the boom tooth support wheel is composed of a boom fan gear and a support wheel attached thereto (see FIG. 5).
  • the boom fan gear is coaxial with the hanging weight point, and the support wheel on the boom fan gear has no teeth.
  • a wheel frame is radially extended at the side flange, and a built-in round wheel is used as the support wheel.
  • the wheel wheel axis is parallel to the force difference wheel wheel axis.
  • This gear set is designed to stabilize the rotating fulcrum of the hanging pestle by fixed fan gears with a radius of 2: 2 (circle points of the fan gear with a pitch circle radius of! ⁇ ), So that the rotating fulcrum of the boom does not cause slippage.
  • the radius of each gear where the lower end of the two gears is located is called the starting edge of each gear;
  • the first and second teeth of the boom sector gear with a radius of ⁇ are calculated from the starting edge, and the tooth width of the first tooth from the starting side is calculated from the fixed side of the fixed sector gear with a radius of r 2 .
  • One-half of the normal tooth width is weak, and its arrangement is unfolded (see FIG. 9).
  • the hoisting pendant uses the node of the gear set as the fulcrum and is located on the edge of the force difference rim to the hanging weight.
  • the axis of the upper end of the hanging pestle with overlapping hammer points is the resistance point.
  • the moment force is used to move the other hammers of the wheel set to the combined force at this point.
  • the lower hammer is transferred to the same force through the outside of the force difference wheel.
  • the force can be achieved by suspending the weight of the hammer. At this time, after the coupling effect of the above gear set is completed, and before the end of the specific range, the freely rotatable support wheel on the suspender tooth support wheel must be externally connected and detoured with a larger center angle and a radius of the fixed sector gear wheel.
  • the torque on the shaft of the differential wheel is zero. After that, the torque of the weight on the shaft of the differential wheel is not zero, which is offset from the original torque.
  • the zero boundary (see Figure 1).
  • the weight is at a standard position angle of 270 °, the torque on the shaft of the force difference wheel is zero again. At this time, the weight is at the lowest position. Then, the weight is moved to a high position and reused in the same way as above. In this process, the torque of the power-consuming differential wheel set is minimized. Therefore, the position of the fixed sector gear should be the same as the path of the lifting point of the hanging weight of each force differential wheel from the lowest to the highest. On the other hand, the position that can give the maximum output in this case should be determined by test method.
  • the angle formed by the connection between the upper and lower axes of the boom and the starting edge of the fan gear of the hanging pestle depends on the starting angle at which the weight is transferred to a higher place; And the radius of the boom fan gear! ⁇
  • the opening angle depends on the opening angle of the fixed sector gear.
  • Each rotation shaft of many force differential wheels is connected in series to form a force differential wheel group.
  • the rotating shafts of the force differential wheel sets that is, the rotating shafts of the different force differential wheels are connected in series.
  • the head end differential wheel which starts from either end of the two ends of the rotation axis of the force differential wheel set, is sequentially arranged to the end end differential wheel of the other end.
  • the adjacent two force differential wheels each have their rotation axis starting from the regular polygonal equivalent point. The position of the line segment perpendicular to the axial direction and the plane passing through the point where the shaft of the force difference wheel and the point end of the force difference wheel are smaller. The smaller angle between the two (line segment and plane) is in the force differential wheel set.
  • the force differential wheel set constituted by the above description, wherein most of the weights will fall from a height along a certain trajectory around the axis of the force differential wheel, and the torque will be generated by using the lever principle to supply other force differential wheel weights through the warp.
  • the lowest point from the vertical line of the rotation axis of the force difference wheel is turned to a high position on the other side of the vertical line. After each weight passes the lowest point, it is necessary to use the torque generated by the weight dropped from a height to raise the weight to a certain height, and then input a larger torque, still based on the principle of leverage.
  • the lower weight is transferred to directly above the fulcrum J, and thereafter, the weight is mechanically applied to the hanging weight by another lever to generate a moment. Repeatedly, it drives the entire force differential wheel set to rotate continuously, and can output power to make other machinery run.
  • a single force differential wheel has different supply and demand moments at each angle, it is necessary to combine each of the single force differential wheels at different angles to form a force differential wheel set.
  • the entire force differential wheel set can output stable power to the outside.
  • One circle is 360 °, then the angle between the two adjacent hanging hammer points on the shaft of the force difference wheel is 360 ° ⁇ 62
  • the angle is one degree. point arrangement method and the like, to give the force of a differential gear set L ⁇ , containing 60 L of this force differential gear according to the present embodiment is selected i.e. the number of 1 L round poor.
  • the headend force difference provided wheel is located by the peer In the horizontal axis of the differential wheel and the horizontal plane on the right, the smaller angle between the equivalent point on each differential wheel and the axis of the differential wheel through the differential axis and the horizontal plane on the right is projected to The included angle ⁇ on the plane perpendicular to the rotation axis of the force difference wheel will be determined by 0 at the head.
  • plane position and force difference wheel shaft constituted of peers should start plane ⁇ L; L arranged so after six cycles, after the L-peer ⁇ multiplexed back to the headend force before the first cycle The position of the peer.
  • ⁇ angle is 0 ° (head-end force difference wheel), 15. , 30 °, 35 °, 40 °, 50 °, 59.
  • Each L-difference wheel (end-difference wheel) is represented by the L-hanging weight point ⁇ as the equivalent point.
  • T 3 . ⁇ ⁇ 4 The calculation is to suspend the hammer point from the standard position angle of 30 °. Move to the standard position angle of 40 ° as the basis, but in reality, only T 3Q ⁇ T 37 are used , and the remaining T 38 ⁇ T 4 . All are omitted, and when the angles that are still within a specific range thereafter should be used, the weight is applied to the hanging weight point by another lever mechanism to obtain the torque on the rotating shaft of the differential wheel. See the subsequent calculations for details.
  • the included angle between the boom suspended by the weight at this point and the axis passing through the pestle and the horizontal plane on the right side of the boom is minus 90 degrees from the horizontal plane (see Figure 8).
  • the weight point is turned to the standard position angle of 40 °, the weight suspended at this point has been transferred to the same force difference wheel which is 100 ° higher than the horizontal level of the weight point where the weight difference is passed through the standard position angle of 40 ° (Standard position angle) on the rim.
  • the horizontal plane of the hanging weight point is parallel to the horizontal plane passing through the rotation axis of the differential wheel, and is included in the horizontal position of the differential wheel and the standard position angle of the differential wheel by 40 °.
  • the radial plane section of the force difference wheel is observed; the radial cross section above the rotation axis of the force difference wheel and the rotation axis and the half plane on the right side of it are small.
  • the included angle is geometrically smaller than the radial cross section below the suspension weight point at the standard position angle of 40 ° of the force difference wheel, and the smaller included angle formed by the half plane to the left of this point forms the L internal misalignment angle ⁇ ,
  • the former is 40.
  • the latter is also 40. ;
  • the standard position angle of the force difference wheel 40 Hang the weight point, and connect it to the standard position angle of 100.
  • the angle 60 is the apex of the hanging weight point with the standard position angle of the differential wheel of 40 °.
  • the inner offset angle L 40 ° is subtracted, and 20 ° is left. This is the standard position angle of the connecting force difference wheel 40.
  • the standard position angle 40 between the weight of the hanging weight and the suspension rod between the weight at the standard position angle of 100 ° and the self-supporting differential wheel. Smaller weight hanging point and the angle between the left horizontal surface; L is small and this angle ⁇ complementary angle of 160 °, and the negative 90.
  • the small included angle formed by the connection between the two axes and the starting edge of the boom fan gear is just the corner of a regular triangle, so the angle is 60 °; and when the hanging weight point is turned to the standard position angle 40.
  • the boom sector gear rotates 240.
  • the arc length must be equal to the 10 ° arc length of the fixed sector gear, so that:
  • the length of the weight 1 suspended from the center of the shaft to the rotation pivot of the boom (that is, the node of the two tangent circles of the gear set) S 3Q can be obtained by using the cosine theorem, and the rest can be deduced by analogy to get the general formula:
  • ⁇ 1 is the angle that the heavy hammer and the rotating fulcrum of the hanging pestle extend to the shaft of the hanging rod.
  • ⁇ L is the smaller angle of 60 ° formed by the connection between the upper and lower two axis of the boom and the starting edge of the fan gear of the boom; when the standard position angle of the force difference wheel is 40 °, the upper and lower axes of the boom are connected.
  • the smaller included angle between the line and the end of the fan sector gear is also exactly the angle of a regular triangle of 60 °, but 6 1 is a larger included angle
  • the value of each length S in the above column projected to the horizontal plane passing through the fulcrum and the fulcrum of the weight (node), and the moment obtained by multiplying the weight of the weight Mg should equal the same node as Node to hanging weight point length! ", Is the moment generated by the moment arm and the hanging weight point is the resistance point; if this moment is divided by the radius of the boom fan gear ⁇ , the period during which the weight is transferred from the low place to the high place through the gear set,
  • the force F exerted by each weight on the flange point of the force difference wheel flange is as follows:
  • Each value from F to 4Q is the force applied to the hanging weight point connected to each weight hammer during the action of the gear set when the weight hammer is transferred from low to high.
  • the direction of this force is the same as the radial direction of the force difference wheel. Vertical; if F is positive, the direction of F is the same as the rotation direction of the force difference wheel; if F is negative, the direction of F is opposite to the rotation direction of the force difference wheel.
  • F 3 To F 4 .
  • the torque T produced by each value to the shaft of the force difference wheel is F 3 .
  • To the product of F 4Q and R, the final moment is obtained. But only T 3 is taken .
  • ⁇ T 37 is as follows:
  • the hanging weight point K is also transferred to the standard position angle 37.5.
  • the mechanical action of the two front and rear levers also uses this standard position angle of 37.5.
  • the weight is located directly above the fulcrum J, so the length H from the center of the weight to the fulcrum J is perpendicular to the horizontal plane (or r 4 ) passing the hanging weight K, forming an oblique length R Right-angled triangle on the side ( Figure 10), so
  • r 4 is parallel to the horizontal plane passing through the rotation axis of the force difference wheel, and both are passed through
  • the radius R of the force difference wheel of the rotating shaft and the hanging weight point K (see FIG. 10)
  • the smaller angle formed by r 4 and R is, for the smaller angle formed by the horizontal plane and R, Into the wrong angle, both of them are 37.5 °, according to the cosine theorem, the radius r 3 of the fixed sector circle is:
  • the moving wheel set Due to a torque difference, the moving wheel set has 360 weights, and each weight generates a torque on the shaft of the force difference wheel. Therefore, among the 60 differential wheels in order from the front differential wheel to the final differential wheel, each of the six weights in the differential wheel is assigned a different number from 1 to 6 .
  • the representation method of the torque produced by the same numbered hammers on the shaft of the force difference wheel is as follows:
  • the standard position angle of each force application point to T 29 is 0. To 29. Therefore, ⁇ 3 is from 0 ° to 29. ;
  • the standard position angle of each force application point from T 2l2 to T 269 is from 212 ° to 269 °, so ⁇ 3 is from 32. To 89 °;
  • T MgRCos ⁇ 3
  • the standard position angle of each force application point is also specified to be greater than 90. .
  • Mg is a positive value (that is, the same direction as the rotation of the force difference wheel); at 90 ° or 270. When the torque is zero, the remainder is negative.
  • each weight is exerted on the flange of the force difference wheel at different angles to suspend the weight point of the force difference wheel by T. Up to T 359 ,
  • the total output torque difference wheel group, L is the subtotal ⁇ force difference values of the or each wheel torque by adding the same number L total weight moment ⁇ addition, both available 722. 4688MgR, this value still needs to supply the L moment difference value of the friction and stray losses of the moving wheel set ⁇ itself.
  • the approximate calculation is as follows:
  • Friction L torque difference
  • Heavy hammer No. 4 11 Fixed sector tooth round

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Description

力矩差值动轮组
技术领域：
本发明涉及一种力矩差值动轮组（参阅图 2) , 简称力差动轮 组， 尤其是将物理学基本原理应用于杠杆组合机械中， 而进行能 源形式转换的动力机械.
背景技术：
人类对取之不尽， 用之不竭的能源非常向往， 自中古时代即 开始寻求制作永久的机构， 但均告失败。 产业革命后， 对能源的 需求日益增加， 大量开采煤炭、 石油等天然石化燃料的结果， 于 是自一九七三年以来发生了两次能源危机， 之后人类开始致力于 其它能源的开发， 有太阳能、 风力、 地热等等， 然而此类能源不 是因地区条件限制， 就是因效益不良， 而不能广泛应用， 而核能 又因众所周知的因素而遭人类排斥。
发明内容：
因此， 目前所寻求的其它能源需能符合取之不尽、 用之不竭 与不污染自然环境的双重条件， 才能为大众接受。 本发明的物件 力差动轮组遂应运而生， 它可满足上述双重条件， 可舒解能源的 危机。
力差轮（参阅图 3,图 4为图 3的反面图）是若干同轴杠杆的集 合体， 也是构成力差动轮组的基本单元， 每个力差轮是由一个转 轴水平贯穿两个半径为 R的内接正多边形结构形成， 而此二正多 边形结构以相对间距略大于重锤长度 L的轴向距离固定于转轴上; 将若干个半径为 R/2, 长为 L, 密度为 D, 圆柱轴向与力差动轮转 轴平行的圆柱体即重锤两端凸出的轴以长为 R的吊杆沿圆柱体的 径向将其吊起， 而吊杆的另一端分别以等距挂于二正多边形结构 的二个对等顶点， 吊杆上端的水平贯穿轴靠固定扇形齿圆轮的一 端称为吊杆齿支轮 12的结构， 其中有以该轴心为圓心、 节圆半径 为 ^的扇形齿轮， 在特定范围内的最初若干角度与另一固定扇形 齿圆轮 11中， 以力差轮转轴为圓心、 节圓半径为 r2固定且不转动 的扇形齿轮构成 +r^R的外接齿轮组；而于特定范围内的其它部 份， 吊杆齿支轮上可自由转动的支轮, 则需外接于固定扇形齿圆 轮中半径为 r3的固定扇形圆轮。
本发明是将物理学的基本原理应用于杠杆组合机械中， 而进 行能源形式转换的动力机械， 本发明的特征是将物体重量或体积 因素（适用水中可得浮力） 而得的力作为杠杆组合机械中原始力 矩的力的来源， 而在杠杆组合机械的每个单元动轮中， 在特定范 围内， 通过耦合作用、 杠杆原理， 将原始力矩转变为最终力矩， 然后使原本力矩为零的界线偏移（参阅图 1) , 汇总偏移界线两边 所有最终力矩与特定范围外的原始力矩得到净力矩， 成为将转动 动能作为输出的杠杆组合机械。
在本发明所述每个单元动轮中的特定范围内通过耦合作用， 可使力矩臂随之改变， 并利用杠杵原理， 将原本作负功的物体转 移至作正功之处。
本发明的优点为：
因为万有引力力矩而得的能量是伴随宇宙物体存在的天然能 源， 故由力差动轮组将万有引力所转换成的旋转动力也是取之不 尽、 用之不竭的能源。
力差动轮組， 是以万有引力力矩为其本身动力的来源， 不需 其它燃料， 故力差动轮组， 适用于任何环境， 也不会污染环境。 图面说明：
图 1 :零力矩线偏移示意图
图 2 :力矩差值动轮组立体图
图 3 :力差轮正面图、 侧面图、 俯视图
图 4 :力差轮反面图 图 5 :吊杆形状图
图 6 :固定扇形齿圆轮形状图
图 7 :吊杆、 重锤、 圆轮结构体組合示意图
图 8 :齿轮耦合图
图 9 :齿轮展开图
图 10 :吊杆齿支轮与固定扇形齿圆轮作用图
图 11 :吊杆齿支轮与固定扇形齿圆轮作用图 具体实施方式：
固定扇形齿圆轮（如图 6) , 是把二半径、轮缘结构均不相同的 小扇形齿轮、 圆轮， 以同心圆方式， 并接成一较大的扇形齿圆轮 而固定于力矩差值动轮组的各个支架上。 固定扇形齿圆轮， 包括 位于较大扇形齿圆轮一端（与吊挂重锤点接近之侧）具有较小圆心 角、 节圆半径为 r2的固定扇形齿轮， 以及位于较大扇形齿圆轮另 一端具有较大圆心角、 半径为 r3的固定扇形圆轮。 其中， 较大圆 心角的固定扇形圆轮， 是在固定扇形齿轮的基础上， 自固定扇形 齿轮终边（与吊杆齿支轮分开之侧）起， 以同一圆心为圆心、 r3为 半径， 顺着力差轮转动方向， 张大其圆心角， 在半径 r3的圃周上 不设置物体。 此扇形圆轮始边（与吊杆齿支轮接近之侧）与固定扇 形齿轮终边重合， 扇形面积不重叠， 且均固定于同一平面内， 对 地速度也为零。
吊杆的形状参阅图 5, 其纵向的上下轴心两点间的距离为 R, 以与正多边形连接的端为上端， 与重锤连接的端为下端。 其上端 的轴需与力差轮的吊挂重锤点重叠， 其间贯穿通过该两点并与力 差轮转轴平行的水平轴， 且与吊杆形成一体， 以使吊杆可以此轴 为中心，在与重锤轴向垂直的平面内旋转；重锤两端的任一端凸出 的圆柱轴心穿过下端的轴承， 与另一吊杆在重锤的另一端以同一 方式共同吊起同一重锤（参阅图 7)。 吊杆上端的水平贯穿轴靠固 定扇形齿圆轮的一端的， 是名为吊杆齿支轮的结构。 吊杆齿支轮 由吊杆扇形齿轮与附设其上的支轮构成（参阅图 5)， 吊杆扇形齿 轮与吊挂重锤点同轴， 其上的支轮自吊杆扇形齿轮没有轮齿侧的 轮缘处径向延伸出一轮架， 内置圆轮， 此圓轮即为支轮， 圆轮轮 轴与力差轮轮轴平行。 吊杵齿支轮中， 有以水平贯穿轴为圓心、 节圆半径 rl的吊杆扇形齿轮， 在特定范围内的某些角度与另一固 定扇形齿圆轮中的固定扇形齿轮， 以力差轮转轴为圓心、 节圆半 径为 r2构成 ri+r2=R的外接齿轮组（参阅图 8)。该齿轮組旨在通过 半径为 3：2的固定扇形齿轮以稳住吊杵旋转支点（节圆半径为 ！^的 扇形齿轮圆周各点）， 不致使吊杆的旋转支点作用时发生滑动现 象， 而非用以传达动力；换言之， 吊杆扇形齿轮的下端与固定扇形 齿轮的下端开始接触耦合时（此时二齿轮下端所在的各齿轮半径， 均称为各该齿轮的始边；为使二齿轮便于耦合起见，分别将半径为 ！^的吊杆扇形齿轮自始边起算第一齿、 第二齿， 与半径为 r2的固 定扇形齿轮自始边起算第一齿的齿宽， 定为正常齿宽的二分之一 弱， 其排列展开图， 参阅图 9) , 其后直至二齿轮分离前， 该吊杵 即以齿轮组的节点为支点、 位于力差轮缘而与吊挂重锤点重叠的 吊杵上端轴心为抗力点， 以力矩差值动轮组其它重锤应用杠杆原 理而施于该点的合力， 将低处的重锤经由力差轮的外侧， 转移至 同一力差轮而在新订支点 J正上方。 此后， 为确保能获得更大的 输出， 必须改用以此新订支点 J为支点的杠杆机械， 以减緩重锤 绕行吊挂重锤点的速度、 延长杠杆机械作用的时间， 继续对吊挂 重锤点施力而可达到目的。 此时， 自上述齿轮组耦合作用完成后， 直至特定范围终了前， 须使吊杆齿支轮上可自由转动的支轮外接 且绕行于固定扇形齿圆轮中较大圓心角、 半径为 r3的固定扇形圆 轮轮缘；吊杵齿支轮上的支轮与固定扇形齿圆轮的固定扇形圆轮 两者外接的点（即新订支点 J) , 距同一吊杆所连吊挂重锤点（后例 定为抗力点 K)间的长度（后例定为 r4)， 加上固定扇形齿圆轮中固 定扇形圆轮半径 r3的长度， 二长度的和， 须大于力差轮正多边形 结构各吊挂重锤点外接圓半径 R的长度。 如此， 即形成支点不相 同的另一杠杆机械； 在此杠杆机械中， 吊杆齿支轮上， 在吊杆扇 形齿轮无轮齿侧，径向延伸所作轮架的长度越短（其上支轮的半径 也随之变短）， 则力矩差值动轮组的效率越高。
当重锤被转移至新订支点 J 正上方时， 对力差轮转轴的力矩 为零， 此后各点的重锤， 对力差轮转轴的力矩不为零， 此即偏移 了原本力矩为零的界线（参阅图 1)。 当重锤位置在标准位置角 270°时， 对力差轮转轴的力矩又为零， 此时重锤位于最低处， 其 后， 再以前述方法将重锤移至高处重复使用， 周而复始。 于此过 程中， 以消耗力差动轮组的力矩至最小程度为原则， 因此， 固定 扇形齿轮的位置， 应与每一力差轮吊挂重锤点由最低处上升至最 高处的路径同側， 其能使本案有最大输出的位置， 应以试验法求 之。
吊杆上下二轴心的连线与吊杵扇形齿轮始边所成较小夹角的 角度（本案所取的角度均为机械角）， 需视重锤转移至高处的起始 角度而定；而吊杆扇形齿轮的半径！^与张开的角度，均视固定扇形 齿轮张开的角度而定。
将许多力差轮的各个转轴以串联方式接续， 即组成一力差动 轮組。 力差动轮组的转轴亦即各个力差轮转轴串接而成。 以力差 动轮组转轴两端的任一端为首起算的首端力差轮依序排列至另一 端的末端力差轮， 其相邻二力差轮上， 各自其转轴起至正多边形 对等点位置所成垂直于轴向的线段， 与通过力差轮转轴及首端力 差轮对等点的平面， 二者（线段与平面） 所夹角度的较小者， 在 该力差动轮组上由首端至末端视之（以下各种度量、 方向、 转向皆 以此为准），均以顺时针或逆时针走向，将由首端的 0度以相等（等 差）间隔排列方式递增至末端力差轮中任何相邻二吊挂重锤点对 力差轮转轴所张的角度；而末端力差轮各点经此间隔排列后，该点 的位置需与首端力差轮自原对等点位置起算沿同一时针走向的连 续二相邻吊挂重锤点间位置相同的对等点位置重合。
由以上说明所构成的力差动轮组， 其中多半数的重锤将由高 处沿一定的轨迹绕力差轮转轴落下， 利用杠杵原理而产生力矩， 供给其它力差轮重锤在通过经力差轮转轴的垂线起的最低处转至 该垂线另一侧的高处之用。 每一重锤经过最低点后， 即需利用由 高处落下的重锤所产生的力矩以提升该重锤至某一高度后， 再输 入更大的力矩， 仍以杠杆原理由齿轮组的作用将低处的重锤转移 至支点 J的正上方， 其后， 重锤则以另一种杠杵机械施力于吊挂 重锤点而产生力矩。 周而复始遂带动整个力差动轮组旋转不息， 并可对外输出动力， 使其它机械运转。
因单一力差轮在每一角度， 其供需力矩的情形并不相同， 故 需集合每一个供需力矩情况不同， 且位于不同角度的单一力差轮 而组成力差动轮組， 除可使该力差动轮组的各个力差轮彼此之间 自行调配力矩的供需情况外， 更可使整个力差动轮组对外输出平 稳的动力。 现举例加以说明：
在力差轮半径为 R的圆周上选取相邻二 L吊挂重锤点 1的弧长 与半径 R相等时的 L吊挂重锤点 数为 2 π Κ / Κ=2 π =6. 28， 取整 数 6为每个力差轮所具有的 L吊挂重锤点，数。一个圆周为 360 ° , 则相邻二吊挂重锤点间对力差轮转轴所张的角度为 360 ° ÷6二 60
。（此亦即为 L正六边形 Ί)， 其各 L顶点 1即为 L吊挂重锤点 Ί。
若以相邻二力差轮所属对等点间对力差轮轴所张开的较小夹 角， 投影至与力差轮转轴垂直平面上的角度均为一度， 按照前迷 的力差轮对等点排列法， 则得一 L力差动轮组 Ί， 含有 60个 L力差 轮 此亦即本例所选取的 L力差轮 1数量. 设首端力差轮的对等 点位于通过力差轮转轴及其右侧的水平面内， 则每个力差轮上的 对等点与通过力差轮转轴及其右侧的水平面间对力差轮转轴的较 小夹角， 投影至与力差轮转轴垂直的平面上的夹角角度 Φ , 将由 首端的 0。每经过一个力差轮即增加一度， 至末端者为 59 ° , 再 回至首端的应为 60 °而为一 L排列循环 而 Φ角， 均以该次循环 开始时， 首端力差轮对等点应在的位置与力差轮转轴所构成的平 面为 L起始平面 Ί ;如此经过六次 L排列循环，后，该 L对等点 Ί复回 至第一次排列循环前首端力差轮对等点的位置。 参阅图 2， 自左 下角起至右上角依序为： Φ角为 0 ° (首端力差轮）、 15。、 30 °、 35 °、 40 °、 50 °、 59。（末端力差轮）的各 L力差轮，为代表， 其 中以 L吊挂重锤点 Ί为对等点。
以下为求得 Τ3。~ Τ4。的演算， 以吊挂重锤点自标准位置角 30 。移至标准位置角 40 °为基础， 但实际上， 只取用其中 T3Q ~ T37， 其余的 T38 ~ T4。均略去不用， 而应采用与此后仍在特定范围内的各 角度时， 重锤均以另一杠杆机械对该吊挂重锤点施力， 进而得到 对力矩差值动轮组转轴的力矩， 详见后续的演算。
假定固定扇形齿轮的下端与上端， 分别位于以力差轮转轴为 原点并以通过该转轴及其右侧的水平面起（凡自此等位置量得的 角度， 称为 L标准位置角 1 ) 30。到 40。的范围内， 亦即在此 10。 的范围内， 应将位于标准位置角 30°吊挂重锤点所连的重锤转移 至同一力差轮标准位置角 100。处之轮缘上（参见图 8与图 10 中 圆点虚线所示者）。 当吊挂重锤点转至标准位置角 30。时， 该点 所吊挂重锤的吊杆与通过吊杵转轴及其右侧的水平面二者间对吊 杆转轴的夹角为自水平面起算负 90度（参阅图 8) , 而当吊挂重锤 点转至标准位置角 40 °时， 该点所吊挂的重锤已被转移至较通过 力差轮标准位置角 40 °吊挂重锤点的水平面为高的同一力差轮 100° (标准位置角） 处的轮缘上。 作通过力差轮标准位置角 40。 吊挂重锤点的水平面，此水平面与通过力差轮转轴的水平面平行， 并均被包含通过力差轮转轴与力差轮标准位置角 40 °吊挂重锤点 且与力差轮转轴平行的径向平面所截；则由首端力差轮观察，在力 差轮转轴以上的径向截面与该转轴及其右侧的半平面所构成较小 的夹角， 在几何学上与在力差轮标准位置角 40°吊挂重锤点以下 的径向截面及该点左侧的半平面所构成较小的夹角形成 L 内错角 Ί, 前者为 40。， 后者也为 40。；又在以力差轮转轴轴心、 力差轮 标准位置角 40。吊挂重锤点， 及该点所连接且位在力差轮标准位 置角 100。轮缘上的重锤轴心三处为顶点所构成的平面正三角形 中， 由以力差轮标准位置角 40°吊挂重锤点为顶点的角 60。内扣 除 L内错角 Ί40°， 尚余 20 °, 此即为连接力差轮标准位置角 40 。吊挂重锤点及在标准位置角 100°处重锤间的吊杆与自力差轮 标准位置角 40。吊挂重锤点及其左侧水平面间的较小夹角；而此 L 较小夹角 Ί的互补角为 160°， 与前述的负 90。角合并， 则得齿轮 作用期间， 重锤对地旋转 160 - （ -90。）=250 °， 对 L力差轮 Ί 旋转 250 - (40° - 30°) =240
当吊挂重锤点转至标准位置角 30°时，吊杆扇形齿轮（半径为 r 与固定扇形齿轮（半径为 r2)开始接触耦合 (Γι+ι:2=Ι ， 此时吊杆 上下二轴心的连线与吊杆扇形齿轮始边所成较小的夹角， 恰为正 三角形的一角， 故其角度为 60°;而当吊挂重锤点转至标准位置 角 40。， 二齿轮作用完毕时， 吊杆扇形齿轮旋转 240。的弧长必 须等于固定扇形齿轮 10°的弧长， 依此得：
2πΓι250ο-(40ο-30 2πΓ240ο-30°
360 360
240Γ!=10Γ2
Figure imgf000010_0001
中得 rt-R / 25
在力差轮标准位置角 30°吊挂重锤点所吊挂编号为 1 的重 锤， 由其轴心至其吊杆旋转支点（亦即齿轮组两节圆相切的节点） 间的长度 S3Q可用余弦定理求出， 其余类推， 可得通式：
Figure imgf000010_0002
Figure imgf000011_0001
其中 Θ 1为重锤与其吊杵旋转支点对吊杆转轴所张的角度。 于力差轮标准位置角 30。时， Θ L即为前述吊杆上下二轴心连 线与吊杆扇形齿轮始边所成较小的角 60 ° ;而在力差轮标准位 置角 40 °时， 吊杆上下二轴心连线与吊杆扇形齿轮终边所成较 小的夹角也恰为正三角形的一角 60 °, 但 61则为较大的夹角
360° -
Figure imgf000011_0002
Q, 亦即 s30 时的 60。起， 其后每次皆以 240。 ÷10。二24°的等差级数递增至 S40 时的 300°, 故得：
V626 - 50 X 0.5 =0.981R 626 - 50 χ 0.1045 =0.997R
Figure imgf000011_0003
S 32=— -^626 - 50 C ^ 108° = ^ V626 + 50Sl'nl 8° =^ 626 + 50 χ 0.309 二 1.014R
Figure imgf000011_0004
=1.028R
Figure imgf000011_0005
.037R
Figure imgf000011_0006
=1.04R
Figure imgf000011_0007
1.037R
Figure imgf000012_0001
=1. 028R
S38=— ^626 - 50Q?5252° =— 626 + 72° = ^ 626 + 50 x 0.309 25 25 25
=1. 013R
Figure imgf000012_0002
=0. 996R
Figure imgf000012_0003
=0. 98R
按照杠杵原理， 将上列各长度 S投影至通过该吊杆、 重锤旋转支 点（节点）的水平面的值， 乘以重锤的重量 Mg后所得的力矩， 应等 于以同一节点为支点、 节点至吊挂重锤点长度！",为力矩臂、 吊挂 重锤点为抗力点，所产生的力矩；若将此力矩除以吊杆扇形齿轮半 径 ^， 即得重锤由低处经由齿轮组而转移至高处的期间， 各该重 锤施于力差轮轮缘吊挂重锤点的力 F， 其通式为：
Ώ_ MgSCos 02 _ MgSCos β2 _ 25 ^ _ n _Μσ 25 " r
F -— ~~― - ^ MgSCos θ -^^ Cos θ2 其中 g为重力加速度， M为重锤质量， θ 2为上述求得的各距离长 度 S与通过节点（支点）及其右侧的水平面间的较小夹角。 当吊挂 重锤点转至标准位置角 30度时， 由 Γι、 R、 S3。三边所构成的三角 形中（R为吊杆的长）， 若1?、 S3。二边夹角（Γι所对的角）甚小时， 其 正弦值与该角的弧度相等， 而该角所对的弧长可视为！^在水平面 上的投影值， 水平面与吊杵扇形齿轮始边 Γι的较小夹角和固定扇 形齿轮始边的标准位置角形成同位角， 均为 30°, 故得弧长
r!CosSO^Sao B，
6 = (r,Cos30 ° ) /
Figure imgf000012_0004
虛 =2。 (此即 ^所对的角度）；又该三角形三个内角和为 180。， 已知 与 S3Q二边所对的角分别为 2 °与 60°， 则 R边所对的角度为 180 。 - 2。 - 60 ° = 118 °，此角扣除通过支点水平面与 ^的较小夹角 (同位角） 30 °后， 余 88。， 又因此 88°角是自通过支点及其右侧 的水平面起以顺时针走向计的， 故为 -88 °角（参阅图 8)。 同理， 可得当吊挂重锤点转至标准位置角 40°时， 支点已移至二扇形齿 轮终边成一直线的交点处， 而通过该支点及其右侧的水平面， 与 S4。所成的较小夹角为 158°, 故得 62在本例中的范围可订为 -88 。 θ 2 158 °， 亦即自 S3。的 - 88。起， 其后每次皆以 [158。 - (- 88。）] ÷10。=24.6。=24。36，的等差级数递增至 S40时的 158 °， 将各 θ2的值代入 F的通式中， 并令 F=Mg方向如为顺时针走 向者为负值， 逆时针走向者为正值， 依此亦即当 -90°〈62<90。 时 F为负值， 90°〈θ2<270°时 F为正值， 得：
F3。= - Mg^°Cos (-88。） =- Mg 25 x 0· χ 0,0349—0- 9Mg
R R
F31= - Mg^&iCos (-63。24，） =_Mg 25 x。· χ 0.45=- 11.3Mg
R R χ 0.78= - 19.8Mg
Figure imgf000013_0001
F33= - Mg Co s (- 14。 12，） =-Mg 25 xL mR χ 0.97= - 25Mg
R R
F34= - Mg^iCos (10o24，）=- Mg25xL χ 0.99= - 25.7Mg
R R
F35= - Mg^iCos (35°) =— Mg 25x1' x 0.8192= - 21.3Mg
R R
F36=― Mg^^Cos (59°36，） =-Mg25xl'0 χ 0.51= - 13.3Mg
R R x 0.11=- 2， 9Mg
Figure imgf000014_0001
F38= - Mg^ Cos (108°48，） =Mg¾ Sin (18。48，）
R R
^25x1.013^ x o 32=8. l g
R
F39= - Mg^ Cos (133。24，） =Mg^^Sin (43。24，）
R R 二 Mg25x0'9 x 0.68=16.9Mg
R
F40= - Mg^^Cos (158。） =Mg^^Sin (68。）
R R 二 Mg25x()' x 0.9272-22.7Mg
R
以上的 F3。至 F4Q各值为重锤由低处转移至高处时， 于齿轮组 作用期间施于各该重锤所连接的吊挂重锤点的力， 此力的方向均 与力差轮的径向垂直；若 F为正值，则 F的方向与力差轮的旋转方 向相同， 若 F为负值， 则 F的方向与力差轮的旋转方向相反。 以 上 F3。至 F4。各值对力差轮转轴所产生的力矩 T, 即为 F3。至 F4Q各值 与 R的乘积， 得最终力矩。 但只取用 T3。~T37如下：
T30=F3。R= - 0.9MgR
T31=F31R= - 11.3MgR
T32=F32R= - 19.8MgR
T33=F33R= - 25MgR
T34=F34R= - 25.7MgR
T35=F35R=-21.3MgR
T36=F36R= - 13.3MgR
T37=F37R= - 2.9MgR 由前述求得 S37的算式中， 知重锤吊杆当时已旋转至以该吊挂 重锤点为圆心， 与 +X轴夹角 [228。 - (180。 -37。）]=85。之处。
根据前设：低处重锤由齿轮组转移至新订支点 J正上方时， 吊 杆齿支轮上的支轮， 须外接于固定扇形齿圆轮中半径为 r3的固定 扇形圆轮， 此二圓轮外接的接点， 即为新订支点 J。 令此支点 J 与该点所连吊杆的吊挂重锤点（抗力点） K 间的长度^ ^r^R/ 10 且与水平面平行（图 10)。 首先要求出重锤自吊挂重锤点 K正上方 转移至支点 J正上方的角度 P：由 RSinP=(R/10)得 Sinp=0.1， 故 P =5°45' =5.75。， 因此， 则知重锤自上述的 85 °之处转移至支 点 J正上方的角度为（90。 - 85。）+5.75。 = 10.75 °：而在齿轮组 耦合作用期间， 吊挂重锤点每移转一度， 重锤即绕行该吊挂重锤 点 24 °， 则上列的 10.75。即相当于吊挂重锤点转移 10.75/ 24=0.448 °, 以 0.5°计之。 此即为重锤转移至支点 J正上方时， 吊挂重锤点 K大约也转移至标准位置角 37.5。之处， 而前后两种 杠杆机械作用也以此标准位置角 37.5。为分界：在 37.5°以前为 齿轮耦合作用（以节点为支点的杠杆）所得的力矩， 如前述的 T3。~ Τ37;而在 37.5°之后， 则为吊杆齿支轮上的支轮与固定扇形圆轮 作用（以二圆轮接点为支点的杠杵）所得的力矩。 于是， 自标准位 置角 37.5。起至特定范围终了前（图 11), 出现另一以重锤所在位 置为施力点与支点 J、 抗力点 K所构成的杠杆机械。 在 37.5。时， 重锤位于支点 J正上方， 故由重锤轴心至支点 J间的长度 H与经 过吊挂重锤点 K的水平面（或 r4)垂直， 形成以重锤吊杵长度 R为 斜边的直角三角形（图 10), 故得
^=^R2-r]=^R2-(R/lO)2=^ =^ x 9.9498=0.99498R 在 37.5°角时， r4与通过力差轮转轴的水平面平行， 并均被 经过该转轴及吊挂重锤点 K的力差轮半径 R所截（参阅图 10), r4 与 R所成较小的夹角， 对于上述水平面与 R所成较小的夹角， 形 成内错角， 二者皆为 37. 5 ° , 由余弦定理得知固定扇形圆轮的半 径 r3为：
Figure imgf000016_0001
在以重锤所在位置与 J、 K三点所构成的杠杆机械中， 利用杠杆原 理得一通式： MgHCos a
Figure imgf000016_0002
将 H与 r4的值代入得：
0. 99498RMgCos α =^ FJ Fj=9. 9498MgCos 其中， a为 H与通过支点 J水平面间的较小夹角， 在标准位置角 37. 5。时， a =90 °起算， 标准位置角每增加一度（力矩差值动轮 組旋转一度）， a即减少一度； ^垂直于 r4 (D， Mg为重锤重量。 另外， 该 ^与力差轮半径切线的夹角为 37. 5。（此角度于本例中 为不变的）， 故！^在力差轮半径切线方向上的分量
F=FjCos [90°一 (90。 - 37. 5。） ] =FjCos37. 5。
=9. 9498Mg (Cos a ) Cos37. 5°
=9. 9498Mg (Cos a ) χ 0. 7934=7. 89MgCos a
此 F为施于吊挂重锤点 K且与力差轮半径 R垂直的力， 故此力对 力差轮转轴的最终力矩 T的通式为 T=FR二 7. 89MgRCos
因在标准位置角 37. 5。时， a =90。，所以 37. 5 °时的力矩 T37 5=0, 自标准位置角 38°起， 各该角度相对应的最终力矩如下：
丁38： =7. 89MgRCos89. 5° =7. 89 x 0. 0087MgR=0. 06MgR
=7. 89MgRCos88. 5。 =7. 89 x 0. 0262MgR=0. 20MgR
=7. 89MgRCos87. 5° =7. 89 x 0. 0436MgR=0. 34MgR
Τ 二 7. 89MgRCos86. 5° =7. 89 x 0. 0610MgR=0. 48MgR
TV =7. 89MgRCos85. 5。 =7. 89 x 0. 0785MgR=0. 61MgR
T =7. 89MgRCos84. 5° =7. 89 x 0. 0958MgR=0. 75MgR
T44" =7. 89MgRCos83. 5。 =7. 89 x 0. 1132MgR=0. 89MgR=T;
Figure imgf000017_0001
T 6 --Ί. 89MgRCos81. 5°= =7. 89 x 0. 1478MgR=l. 16MgR=T209
Τ47= :7. 89MgRCos80. 5。: =7. 89 x 0. 1650MgR=l. 30MgR二 T208
Τ48" :7. 89MgRCos79. 50: :7. 89 χ 0. 1822MgR=l. 43MgR=T207
Τ49" :7.謹 gRCos78. 5。: =7· 89 x 0. 1994MgR=l. 57MgR=T206
ΤδΟΖ :7. 89MgRCos77. 5。: =7. 89 x 0. 2164MgR=l. 70MgR=T205 τ51： =7. 89MgRCos76. 5°= =7. 89 χ 0.
Figure imgf000017_0002
:7. 89MgRCos75. 5°: =7. 89 x 0. 2504MgR=l. 97MgR=T203 δ3" :7. 89MgRCos74. 5。: =7. 89 x 0.
Ts r :7. 89MgRCos73. 5°: =7. 89 x 0.
Figure imgf000017_0003
=7. 89MgRCos72. 50: =7. 89 χ 0. 3007MgR=2. 37MgR=T200
Τδ6" :7. 89MgRCos71. 5。: =7. 89 χ 0. 3173MgR=2. 50MgR=T199 τ57: :7. 89MgRCos70. 5°: =7. 89 χ 0. 3338MgR=2. 63MgR=T198 τ58: =7. 89MgRCos69. 5° =7. 89 χ 0. 3502MgR=2. 76MgR=T197 τ59: =7. 89MgRCos68. 5。 =7. 89 χ 0. 3665MgR=2. 89MgR二 T196
： Ί. 89MgRCos67. 5。 =7. 89 χ 0. 3827MgR=3. 01MgR=T195 τ61： =7. 89MgRCos66. 5° =7. 89 χ 0. 3987MgR=3. 14MgR=T194
=7. 89MgRCos65. 5。 =7. 89 χ 0. 4147MgR=3. 27MgR=T193 β3: =7. 89MgRCos64. 5° =7. 89 χ 0. 4305MgR=3. 39MgR=T192 β : =7.讓 gRCos63. 5° :7. 89 x 0. 4462MgR=3. 52MgR=T191 β5: =7. 89MgRCos62. 5°二 7. 89 χ 0. 4617MgR=3. 64MgR=T190
Τθ6: =7. 89MgRCos61. 5°二 7. 89 χ 0. 4772MgR=3. 76MgR=T189
Τβ7" =7. 89MgRCos60. 5。 =7. 89 χ 0. 4924MgR=3. 88MgR=T188 βδ" =7. 89MgRCos59. 5。 =7. 89 χ 0. 5075MgR=4. 00MgR=T187 δ9: =7. 89MgRCos58. 5° =7. 89 χ 0. 5225MgR=4. 12MgR=T186
Τγθ" =7. 89MgRCos57. 5。 =7. 89 χ 0. 5373MgR=4. 23MgR=T185
T =7. 89MgRCos56. 5° =7. 89 χ 0. 5519MgR=4. 35MgR=T184 72 =7. 89MgRCos55. 5。 =7. 89 χ 0. 5664MgR=4. 46MgR=T183 T73- =7. 89MgRCos54. 5° =7. 89 x 0. 5807MgR=4. 58MgR=T182
T74= :7. 89MgRCos53. 5° =7. 89 x 0. 5948MgR=4. 69MgR=T181 τ75= :7. 89MgRCos52. 5° =7. 89 x 0. 6088MgR=4. 80MgR=T180 丁76 = -1. 89MgRCos51. 5。 =7. 89 x 0. 6225MgR=4. 91MgR=T179 77~ :7. 89MgRCos50. 5。 =7. 89 x 0. 6361MgR=5. 01MgR=T178 丁78 = :7. 89MgRCos49. 5° =7. 89 x 0. 6494MgR=5. 12MgR=T177
Τγ9~ :7. 89MgRCos48. 5° =7. 89 x 0. 6626MgR=5. 22MgR=T176
TgO" -7. 89MgRCos47. 5° =7. 89 x 0. 6756MgR=5. 33MgR=T175 τ81= --7. 89MgRCos46. 5° =7. 89 x 0. 6884MgR=5. 43MgR=T174
Τβ2~ :7. 89 gRCos45. 5° =7. 89 x 0. 7009MgR=5. 53MgR=T173
89MgRCos44. 5° =7. 89 x 0. 7133MgR=5. 62MgR=T172
Τ84~ =7. 89MgRCos43. 5° =7. 89 x 0. 7254MgR二 5. 72MgR=T171
Figure imgf000018_0001
81MgR=T170
:7. 89MgRCos41. 5° =7. 89 x 0. 7490MgR=5. 90MgR=T169 β7 :7. 89MgRCos40. 5° =7. 89 x 0. 7604MgR=5. 99MgR=T168 丁88 = :7. 89MgRCos39. 5° =7. 89 x 0. 7716MgR=6. 08MgR=T167 eg- :7. 89MgRCos38. 5° =7. 89 x 0. 7826MgR=6. 17MgR=T166 丁90 = =7. 89MgRCos37. 5C '=7. 89 x 0. 7934MgR=6. 25MgR=T165 τ91： :7. 89MgRCos36. 5° '=7. 89 x 0. 8039MgR=6. 34MgR=T164
Tg2" =7. 89MgRCos35. 5C '=7. 89 x 0. 8141MgR=6. 42MgR=T163
Tg3 = :7. 89MgRCos34. 5C '=7. 89 x 0. 8241MgR=6. 50MgR=T162
T94" =7. 89MgRCos33. 5C '=7. 89 x 0. 8339MgR=6. 57 gR=T151
T95- :7. 89MgRCos32. 5C 、：Ί. 89 x 0. 8434MgR=6. 65MgR=T160
T96" =7. 89MgRCos31. 5C '=7. 89 x 0. 8526MgR=6. 72MgR=T159 丁97= =7. 89 gRCos30. 5C '=7. 89 x 0. 8616MgR=6. 79MgR=T158 丁98
Figure imgf000018_0002
gg1 =7. 89MgRCos28. 5C *=7. 89 x 0. 8788MgR=6. 93MgR=T156
T100 =7. 89MgRCos27. 5 °=7. 89 > ' 0. 8870MgR-6. 99MgR=T155 Tio r =7. 89MgRCos26. 5£ '=7. 89 x 0. 8949MgR=7. 06MgR=T154
Tl02: :7. 89MgRCos25. 5' '=7. 89 x 0. 9026MgR=7. 12MgR=T153
Tl03: =7. 89MgRCos24. 5( '=7. 89 x 0. 9100MgR=7. 17MgR=Tl52
Tl04: =7. 89MgRCos23. 5( '=7. 89 x 0. 9171MgR=7. 23MgR=T151 ΐ05: =7. 89MgRCos22. 5( '=7. 89 x 0. 9239MgR=7. 28MgR=T150
Τΐ06: =7. 89MgRCos21. 5( '=7. 89 x 0. 9304MgR=7. 34MgR=TH9
Τΐ07: =7. 89MgRCos20. 5( '=7. 89 x 0. 9367MgR=7. 39MgR=T148
Τΐ08: :7. 89MgRCosl9. 5£ '=7. 89 x 0. 9426MgR=7. 43MgR=T147
Τΐ09: =7. 89MgRCosl8. 5( '=7. 89 x 0. 9483MgR=7. 48MgR=T146
Τι ιο: =7. 89MgRCosl7. 5ι '=7. 89 x 0. 9537MgR=7. 52MgR=T145
ΤΠΓ =7. 89MgRCosl6. 5( '=7. 89 x 0. 9588MgR=7. 56MgR=T144
Τΐ ΐ2: =7. 89MgRCosl5. 5' '=7. 89 x 0. 9636MgR=7. 60MgR二 T143 π3: =7. 89MgRCosl4. 5( '=7. 89 x 0. 9681MgR=7， 63MgR=T142
Τΐ 14: =7. 89MgRCosl3. 5( ,=7· 89 x 0. 9724MgR=7. 67MgR=T141
Τΐ ΐ5: =7. 89MgRCosl2. 5( '=7. 89 x 0. 9763MgR=7. 70MgR=T14o
Τΐ ΐ6: =7. 89MgRCosl l. 5( '=7. 89 x 0. 9799MgR=7. 73MgR=T139
T 7: :7. 89MgRCoslO. 5( '=7. 89 x 0. 9833MgR=7. 75MgR=T138
Τΐ 18: =7. 89MgRCos9. 5°= :7. 89 x 0. 9863MgR=7. 78 gR=T137 π9: =7. 89MgRCos8. 5。= :7. 89 x 0. 9890MgR=7. 80MgR=T136 ΐ20: =7. 89MgRCos7. 5°- :7. 89 x 0. 9914MgR=7. 82MgR=T135 ΐ2Γ =7. 89MgRCos6. 5。= -7. 89 x 0. 9936MgR=7. 83MgR二 T134
Τΐ22: =7. 89MgRCos5. 5。= :7. 89 x 0. 9954MgR=7. 85MgR=T133
Τ ΐ23: =7. 89MgRCos4. 5。= :7. 89 x 0. 9969MgR=7. 86MgR=Tl32
Τΐ 24: =7. 89MgRCos3. 5°= -7. 89 x 0. 9981MgR=7. 87MgR=T131
Τΐ25: =7. 89MgRCos2. 5°= :7. 89 x 0. 99翅 gR:7. 88MgR=T130
Τΐ26: =7. 89MgRCosl. 5°= :7. 89 x 0. 9997MgR=7. 88MgR二 T129
Τΐ27: =7. 89MgRCosO. 5。= :7. 89 x 1. 0000MgR=7. 89MgR=T128 此后的 T128=7. 89MgRCos ( - 0. 5。） =7. 89MgRCosO. 5°=T 而 Τ129=7· 89MgRCos ( - 1. 5°) =7. 89MgRCosl. 5。=Ί\ 126
依此类推， 直至 Τ211=Τ44=0. 89为止， 此项对应关系， 分别列注于 Τ127至 Τ44各力矩值之后。 最后可知， 本例的特定范围是从标准位 置角 30。起至 211。止，于特定范围内所得上述 T3Q至 Τ211各力矩， 即为最终力矩；其余的均为原始力矩。
因一个力矩差值动轮组有 360 个重锤， 每一个重锤对力差轮 转轴均产生一个力矩。 因此， 现将在由首端力差轮依序至末端力 差轮的 60个力差轮中， 对每一个力差轮中的六个重锤， 各賦予一 个 1至 6数字中不同的编号。 编号相同的各重锤对力差轮转轴产 生的力矩表示法规定如下：
编号为 1的各重锤， 其相对应的各力矩， 定为 Τ。至 Τ5
编号为 2的各重锤， 其相对应的各力矩， 定为！^至^ 1 19
编号为 3的各重锤， 其相对应的各力矩， 定为了^至 179
编号为 4的各重锤， 其相对应的各力矩， 定为 Τ18。至 Τ2239
编号为 5的各重锤， 其相对应的各力矩， 定为丁24。至下2299
编号为 6的各重锤， 其相对应的各力矩， 定为丁3。。至丁3 359
除 T3Q至 Τ211各值已如上述求得外， 其余的 Τ。至 Τ29与 Τ212至 Τ359各 力矩值， 均为以各该重锤圆柱轴心与力差轮转轴轴心间的水平距 离乘以重锤的重量 Mg。 由图 3可知， 该水平距离即为力差轮半径 R在各位置投影至通过力差轮转轴的水平面上的距离 RCos03, θ 3 为 R 与通过力差轮转轴的水平面间的较小或相等夹角；若以数学 式表之， 则为： T=MgRCos 6 3其中
T。至 T29各施力点的标准位置角由 0。至 29。，故 Θ 3由 0 °至 29。； T2l2至 Τ269各施力点的标准位置角由 212 °至 269 ° , 故 θ 3由 32。 至 89° ;
Τ27。至 Τ359各施力点的标准位置角由 270。至 359 ° , 故 Θ 3由 90。 至 Γ ;
在 T=MgRCos Θ 3式中， 也规定其各施力点的标准位置角在大于 90 。而小于 270 °的范围内， Mg 为正值（亦即与力差轮旋转方向相 同）；在等于 90°或 270。时， 力矩为零， 余者为负值。
兹将 L力矩差值动轮组 1中， 各个重锤于各角度施力于力差轮 轮缘吊挂重锤点而对力差轮转轴所产生的力矩， 由 T。至 T359各值，
Figure imgf000021_0001
Figure imgf000022_0001
Figure imgf000023_0001
|Γ|为表内 Τ。至 Τ359各力矩的绝对值。
由以上表列的合计项得知， 力矩差值动轮组的总输出， 为将 各力差轮力矩的 L小计 Ί值相加或各编号相同的重锤力矩 L合计 Ί 相加， 均得 722. 4688MgR, 此值尚需供给 L力矩差值动轮组 Ί本身 的摩擦力与杂散损失的消耗。 概略计算如下：
摩擦力： L力矩差值动轮组1总输入 为上表内各力矩值的绝 对值总和， 即 ^=1133. 8848MgR;若假设滚动摩擦系数为 0. 3%, 则 摩擦力的损失约为
1133. 8848MgR χ 0. 3%=3. 5MgR
又假设杂散损失与摩擦损失相同， 也为 3. 5MgR。
则净输出 W0=722. 4688MgR - 3. 5MgR - 3. 5MgR=715. 4688MgR。
轴效率 =输出净值 /输入总值 χ100%=715. 4688 ÷1133. 8848 χ 100%=63. 09%
而毛效率 =722. 4688 ÷1133. 8848 χ100%=63. 71%
损失约为 63. 71% - 63. 09%=0. 62%
另外， 如 r4的长度越接近 Γι或减小 Z FK , 效率则越高；例如 r4=R / l5， 则力矩差值动轮组的输入与输出均可同时提高， 效率 也可达到 70%。 然而 r4趋近于 或减小 FKFj, 也有其极限值。 各图式零件符号如下:
1 编号为 1的重锤 8： 内接正多边形结构
2 编号为 2的重锤 9： 吊杆
3 编号为 3的重锤 10： 对等顶点或吊挂重锤点
4 . 编号为 4的重锤 11： 固定扇形齿圆轮
5 编号为 5的重锤 12： 吊杆齿支轮
6 编号为 6的重锤 14： 支架
7 转轴

Claims

权利要求
1. 一种力矩差值动轮组，是将物理学的基本原理应用于杠杆組 合机械中， 而进行能源形式转换的动力机械， 其特征是以物体重 量或体积因素而获得的力， 作为杠杆组合机械中原始力矩的力的 来源， 而在杠杆组合机械的每个单元动轮中， 在一范围内通过耦 合作用、 杠杵原理将原始力矩转换为最终力矩、 物体由作负功处 转至作正功处， 进而使原本力矩为零的界线偏移， 汇集此偏移界 线两边所有最终力矩与上述范围外的原始力矩， 得到净力矩， 并 可以转动动能为输出的杠杵组合机械。
2. 根据权利要求 1所述的一种力矩差值动轮组，其特征在于： 力差轮为若干同轴杠杆的集合体， 也为构成力矩差值动轮组的基 本单元， 每个力差轮是由一个转轴水平贯穿两个半径为 R的内接 正多边形结构形成， 而此二正多边形结构是以相对间距略大于重 锤长度 L的轴向距离固定于转轴上；另外将若干个质量为 M, 长为 L, 密度为 D， 圆柱轴向与力差动轮转轴平行的圆柱体即重锤两端 凸出的轴以长为 R的吊杆沿圓柱体的径向将其吊起， 而吊杆的另 一端分别以等距挂于二正多边形结构的二对等顶点， 吊杵上端的 水平贯穿轴的一端是吊杆齿支轮的结构，其中有以该轴心为圆心、 节圆半径为 Γι的扇形齿轮， 在一范围内的最初角度与另一固定扇 形齿圆轮中以力差轮转轴为圆心， 节圆半径为 r2固定且不转动的 扇形齿轮构成 rf r2=R 的外接齿轮组；而在上述范围内的其它部 分， 吊杆齿支轮上可自由转动的支轮， 则需外接于固定扇形齿圆 轮中半径为 r3的固定扇形圆轮。
3. 根据权利要求 1所述之一种力矩差值动轮组，其特征在于： 所述每个单元动轮中的吊杆两端轴心， 与重锤相连的部分为施力 点， 其余部分为抗力点， 另外分别以抗力点与偏向施力点侧的另 一点为圃心， 各置一轮， 以使此吊杆可与二半径、 轮缘结构均不 相同的小扇形齿轮、 圆轮以同心圆但扇形面积不重叠的方式接成 的一个较大的对地固定扇形齿圆轮配合运用， 变更支点位置， 用 不同的支点， 以减緩吊杆重锤绕轴下降的速度， 而延长了杠杵机 械作用时间， 并仍以自然力及利用杠杆原理， 通过耦合作用， 可 使吊杆力矩臂随之改变， 而将原本作负功的物体转移至作正功之 处的一种机械。
PCT/CN2003/000155 2002-03-29 2003-02-27 Groupe de roue dynamique a moment variable WO2003083296A1 (fr)

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Cited By (4)

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Publication number Priority date Publication date Assignee Title
WO2008135248A2 (de) * 2007-05-03 2008-11-13 Friedrich Schmoll Vorrichtung zum antrieb einer welle mittels eines pendels und eines kurbeltriebs
EP2110554A1 (en) * 2008-04-18 2009-10-21 Mexon Laboratorio di Ricerca Tecnologica di Soncin Giancarlo Gravity motor
WO2010035181A2 (en) 2008-09-26 2010-04-01 Ramazan Eryildiz Wheel arm displacing center of gravity
WO2010066246A1 (de) * 2008-12-13 2010-06-17 Egon Frommherz Aggregat zur nutzung alternativer energie

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CN101603490B (zh) * 2009-07-17 2013-03-13 高新潮 用重锤启动的动力机

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WO1997016642A1 (es) * 1995-11-02 1997-05-09 Bolado Ortiz Andres Movimiento de palancas por gravedad
CN1162072A (zh) * 1996-04-08 1997-10-15 孟宪纯 杠杆动力机(永动机)
CN1289009A (zh) * 2000-05-29 2001-03-28 李文生 一种输出扭矩的动力机

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CN1044150A (zh) * 1988-02-04 1990-07-25 戴坚忍 地球重力发电机
WO1997016642A1 (es) * 1995-11-02 1997-05-09 Bolado Ortiz Andres Movimiento de palancas por gravedad
CN1162072A (zh) * 1996-04-08 1997-10-15 孟宪纯 杠杆动力机(永动机)
CN1289009A (zh) * 2000-05-29 2001-03-28 李文生 一种输出扭矩的动力机

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2008135248A2 (de) * 2007-05-03 2008-11-13 Friedrich Schmoll Vorrichtung zum antrieb einer welle mittels eines pendels und eines kurbeltriebs
WO2008135248A3 (de) * 2007-05-03 2009-04-23 Friedrich Schmoll Vorrichtung zum antrieb einer welle mittels eines pendels und eines kurbeltriebs
EP2110554A1 (en) * 2008-04-18 2009-10-21 Mexon Laboratorio di Ricerca Tecnologica di Soncin Giancarlo Gravity motor
WO2009127445A1 (en) * 2008-04-18 2009-10-22 Mexon Laboratorio Di Ricerca Tecnologica Di Soncin Giancarlo Gravity motor
WO2010035181A2 (en) 2008-09-26 2010-04-01 Ramazan Eryildiz Wheel arm displacing center of gravity
WO2010035181A3 (en) * 2008-09-26 2010-08-26 Ramazan Eryildiz Wheel arm displacing center of gravity
CN102203414A (zh) * 2008-09-26 2011-09-28 拉马赞·埃耶尔德兹 使重心移位的轮臂
WO2010066246A1 (de) * 2008-12-13 2010-06-17 Egon Frommherz Aggregat zur nutzung alternativer energie

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