GEARWHEEL MECHANISM FOR THE CONVERSION OF RECI PROCAL MOTION INTO ROTARY MOTION AND VISA VERSA
The supposed gearwheel mechanism for the conversion of forward motion into rotary motion and visa versa is attributed to the sphere of general mechanical engineering, is related to machine and mechanism units ensuring the normal operation and exploitation of machines and mechanisms, and is for the conversion of forward motion into rotary motion and visa versa - rotary motion into forward motion by means of rotating gearwheels only.
The mechanism may be used in astronautics, aviation, shipbuilding, motor industry, motor cycle industry, in the field of mining industry, radio electronic industry, power engineering industry, other industrial branches, in medicine, and in many other spheres of application. The mechanism supposed is ideally suitable for the manufacture of the new type internal combustion engines, processing machines, civil engineering equipment, food production machines, fixing-grasping mechanisms, and etc. The authors have named the mechanism as Kuptsov's mechanism and decided to mark it by this sign.
For the being time a large variety of gearwheel mechanisms is known: from the simplest one-stage gears to the multi-stage gears formed by the consecutive connection of one-stage gears; from the units installed into mechanisms, devises, and machines to an autonomous unit consisting of a reducer, a gear box, a sun-and-planet gear, and a differential gear.
A gearwheel mechanism using the axial motion of a forge-rolling cylinder for a platen printing press (I.I. Artobolevsky, Mechanisms in modern engineering Volume. IV, Moscow «Nauka», 1981, p. 102) formed out of a pair of bevel pinions - one pinion is fixed to a rotating axis, whereas the other pinion has a finger that is cinematically interacting with the cylinder's slot - may be mentioned as an example of a gearwheel drive. The functional application of this gearwheel drive is limited.
The purpose of this invention is to create as simple as possible gearwheel mechanism that would simplify all mechanical units and mechanisms using connecting rod mechanisms and units (for instance, a internal combustion engine) to convert forward motion into rotary motion.
The gearwheel mechanism for the conversion of forward motion into rotary motion and visa versa consists of a drive shaft with a pair of bevel pinions. The novelty of this invention is the following: one bevel pinion out of the said pair of bevel pinions is fixed to the end of a drive shaft, whereas a crank is fixed to the axis of the other bevel pinion; one end of this crank is immovably fixed to the end of another crank; loosely rotating gearwheels are set on the disengaged ends of the cranks; other cranks are immovably fixed to these gearwheels; loosely rotating gearwheels are permanently engaged with appropriate intermediate gearwheels; intermediate gearwheels have paired bevel pinions that are connected to each other by means of a parasite gearwheel; the said parasite gearwheel is loosely installed in the mechanism's body so that the drive shaft and the axis of the parasite gearwheel are forming the imaginary axis of the mechanism along which the cranks with the gearwheels set on them are positioned; in addition to this, the sizes of radiuses of cranks and set on them freely rotating gearwheels differ; relationship between the radiuses mentioned is the following: the radius of a crank positioned on one side of the imaginary axis is equal to the radius of a loosely rotating gearwheel set on a crank and positioned on the other side of the mechanism, whereas the total sum of crank radiuses is equal to the diameter of intermediate engagement gearwheels.
This invention may cause a turnover in the theory and industry of machines and mechanisms, this mechanism is enabling to use the force obtained and transmitted in the course of forward or rotary motion in the most efficient way, to ensure the long lasting operation of such mechanisms, and to obtain precise uniform rectilinear and complex cycling motions. Besides, the mechanism supposed is converting forward motion into rotary motion and visa versa by means of gearwheel drive systems only. The feasibility to derive the formula of motion of disengaged ends of cranks, to make the disengaged ends of crank pass different distances, to make the disengaged ends of cranks move at different angles 0 degree to 180 degrees should be attributed to the advantages of the mechanism supposed.
The invention is explained in drawings. The schematic diagram is presented in Fig. 1, the diagram of the mechanism's left side is presented in Fig. 2, and the diagram of the mechanism's right side is presented in Fig. 3.
The mechanism supposed consists of drive shaft 1 , which is connected to two cranks 4 and 5 immovably connected to each other by means of gearwheels 2 and 3.
Loosely rotating gearwheels 8 and 9 are set on the ends of cranks 4 and 5, whereas cranks 6 and 7 are immovably connected to gearwheels 8 and 9 appropriately.
Gearwheels 8 and 9 are permanently engaged with appropriate intermediate gearwheels
10 and 11. Gearwheels 10 and 11 are paired with bevel pinions 12 and 13 connected to each other by means of parasite gearwheel 14. A parasite gearwheel is loosely rotating in the mechanism's body 15. Radiuses r; and r2 of cranks 5 and 6 as well as 4 and 7 on each side of the mechanism are appropriately equal, whereas the sum of radiuses of all cranks is equal to the diameter rfj of intermediate engagement gearwheels 10 and 11.
The special features of the mechanism supposed are listed below. In the course of rotating of shaft 1 :
1. Disengaged ends of cranks 6 and 7 may move in different ways;
2. An angle at which the disengaged ends of cranks 6 and 7 move in regard of each other may be anything and extends from 0 degree to 180 degrees;
3. The distances passed by the disengaged ends of cranks 6 and 7 may be different;
4. A torque to shaft 1 is derived by applying force actuating rectilinear motion to the disengaged ends of cranks 6 and 7.
The principle of operation of the mechanism is the following:
Drive shaft 1 is rotated by gearwheels 2 and 3. Gearwheel 3 is rotated by two immovably connected to each other cranks 4 and 5 to the ends of which loosely rotating gearwheels 8 and 9 are fixed, whereas cranks 6 and 7 are fixed to gearwheels 8 and 9, one crank to each gearwheel. Gearwheels 8 and 9 are permanently engaged with appropriate intermediate gearwheels 10 and 11, which start rotating in opposite directions through paired gearwheels 12 and 13 due to parasite gearwheel 14. Gearwheels 10 and 11 are paired with bevel pinions 12 and 13, which are engaged to each other by means of parasite gearwheel 14. The parasite gearwheel is loosely rotating in the mechanism's body 15. In addition to this, the direction of rotation of intermediate engagement gearwheels coincides with the direction of rotation of a paired crank the radius of which is larger. In the course of rotation around their axes, the disengaged ends of cranks 6 and 7 are moving in a rectilinear reciprocate way.
Let us consider the operation of the mechanism.
Since:
2rι + 2r2 = 2r_ ,
where r7 + r = r3 , then the radius Rs of gearwheel 8 is equal to:
Rs = r2.
The radius R$» of gearwheel 9 is equal to:
R9 = r7.
The sum of the radiuses of above mentioned gearwheels 8 and 9 is equal to the radius Ryøof the intermediate engagement gearwheel:
Rio = Rs + R9 = n + r2 = r3.
The radiuses Rs and Rj
> of gearwheels 8 and 9 are not equal and differ from the value r
3/2 by the following value:
Therefore gearwheels 8 and 9, which have:
Rs = r and R? = rj , will make the following number of rotations within one rotation of paired gearwheels 4 and 5:
2 πr
3 + 2 π(2rj - r ) 2 πr
3 + 4 πrj - 2 πr
3 = = 2 n (rotations);
2 πr3 - 2 π(r3 - 2 r2) 2 πr - 2 πr3 + 4 πr2
= 2 n (rotations).
2 πr2 2 πr2
Since intermediate engagement gearwheels 10 and 11 are rotating in opposite directions, the distance passed by gearwheel 8 the radius of which Rs = r2 is diminished by the value Is , which is equal to: ls = 2 π(r3 - 2 2).
The distance to be passed by gearwheel 9 the radius of which is R
9 = rj is increasing by the value I
9, which is equal to:
The disengaged ends of cranks 6 and 7 are shifted from a dead point by means of engagement of gearwheels, therefore the angle between drive cranks may be anything and also may be equal to 0° and 180 °.
The equation of motion of disengaged ends of cranks 6 and 7.
Let us consider both the right and left sides of the mechanism together (Fig. 2 and Fig. 3).
If a crank OA shifts to the angle α (Fig. 2), the point B will shift to the point B , the central point A of gearwheel 9 the radius of which R9 = rt will shift to the point A , whereas gearwheel 10 the radius of which Rio = r3 will rotate in the direction opposite to the rotation direction of the crank OA.
The distance S
y passed by the point B will be equal to:
According to the isosceles triangle OAjBj:
OC = CBj = OAj cos a = AiB cos a; then, -
OB] = OAj cos a + A] B] cos a = r cos a + r2 cos a = 2 r2 cos a.
Sy = 2 r - 2 r2 cos a = 2 r2 (1 - cos a) ;
Since: r2 = r3 - ri , then:
Sy = 2(r3 - rι)(l - cos a);
J = 2 (r3 - rj), provided that a = 0° ; ymin = - 2(r3 - rj), provided that = 180° ;
Smax = 4 (r3 - n) .
If the crank OjA_ in the course of rotation shifts to the angle a (Fig. 3), the point B] will shift to the point B2; the central point A] of gearwheel 8 the radius of which Rs = r2 will shift to the point A2; whereas gearwheel 11 the radius of which R/7 = r3 will rotate in the same direction as the crank OJAJ.
The distance S
y passed by the point Bj will be equal to:
According to the triangle OjA
2B
2
OjC] = CjB2 = OjA2 cos a = A2B cos a, then:
0]B2 = 0]A2 cos a + A2B2 cos a = i cos a + ry cos a = 2 j cos a.
Sy = 2 j - 2rj cos a = 2rt (1 - cos a);
Since: ri = r3 - r2, then:
Sy = 2 (r3 - r2)(l - cos a). ymax = 2(r3 - r ), provided that the angle = 180° , ymin = - 2 (r3 - r2), provided that the angle = 0° .
Smax = 4(r3 - r2).