MECHANICAL DRIVES

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MECHANICAL DRIVES


MECHANICAL DRIVES ARE USED TO PROVIDE A VARIABLE OUTPUT SPEED FROM A CONSTANT SPEED POWER SOURCE OR TO PROVIDE TORQUE INCREASE FOR A VARIABLE SPEED POWER SOURCE AS IN AN AUTOMOBILE.

PEOPLE OFTEN LOOKED FOR CONSTANT TECHNOLOGICAL ADVANCEMENT TO GAUGE THE PROGRESSION OF A PIECE OF EQUIPMENT. ONE NOTEWORTHY EVOLUTION IN THE LAST 50 YEARS IS OF MECHANICAL DRIVE. TRENCHERS USED TO PUT STUFFS IN THE GROUND GRADUALLY SHIFTED OVER THE LAST SEVERAL YEARS TO MECHANICAL DRIVE. MECHANICAL DRIVES USED GEARBOXES, SHAFTS, PULLEYS, CHAINS AND SPROCKETS TO DRIVE THE TRENCHER CHAIN.


ADVANTAGES AND DISADVANTAGES OF MECHANICAL DRIVES


MECHANICAL DRIVES ARE LESS COSTLY THAN COMPETING ELECTRICAL DRIVES AND THEIR CONTROL IS MUCH SIMPLER. THEY ARE USED IN INDUSTRIES RANGING FROM AEROSPACE TO MINING AND HEAVY INDUSTRY. WITH THE ADVANCED TECHNOLOGY, THE WORKING OF MECHANICAL DRIVE HAS BECOME MORE EFFICIENT. THE DISADVANTAGE OF THESE DRIVES IS THAT THEY ARE NOT DURABLE AND CANNOT BE CONTROLLED AS PRECISELY AS ELECTRICAL DRIVES. THEY CANNOT TRANSMIT AS MUCH POWER AS ELECTRICAL DRIVES WHEN VARIABLE SPEED IS ESSENTIAL.

TYPES OF MECHANICAL DRIVES

THE BASIC TYPES OF MECHANICAL DRIVES ARE:

GEARED TRANSMISSION - PROVIDES SPECIFIC FIXED TYPE RATIOS.

BELT DRIVES - PROVIDE FLEXIBILITY IN THE POSITIONING OF THE MOTOR.

CHAIN DRIVES - PROVIDE INFINITELY VARIABLE SPEEDS.

TRACTION DRIVES - PROVIDES ADJUSTABE SPEED WITH RELATIVELY HIGH SPEED.

FEATURES OF MECHANICAL DRIVES

SPECIFIC CHARACTERISTICS ARE CONSIDERED WHILE DESIGNING MECHANICAL DRIVES SUCH AS FOLLOWS:

LOW-STRESS

UNIVERSAL MOUNTING

HIGH-STRENGTH MONOBLAC CASINGS

HIGH-ENERGY EFFICIENCY AND

LOW NOISE LEVEL

THE MONOBLAC DESIGN HAS INCREASED CENTER DISTANCES BETWEEN THE OUTPUT SHAFT BEARINGS, MAKING THE UNIT ABLE TO WITHSTAND SIGNIFICANTLY HIGHER RADIAL LOADING.

MAINTENANCE OF MECHANICAL DRIVES

MECHANICAL DRIVES HAVE INTERNAL SPACES THAT HAVE VOID SPACES WHERE RESIDUES CAN BE DEPOSITED. THE SYSTEM SHOULD BE CLEANED AT REGULAR INTERVALS. CLEAN-IN PLACE (CIP) IS A METHOD DESIGNED AUTOMATICALLY TO CLEAN PIPES AND DRIVES. THIS METHOD IS USED TO CLEAN THE VOID SPACES IN THE DRIVES.

STEPLESS DRIVES:

AN AUTOMATIC STEPLESS TRANSMISSION INCLUDES A DRIVING SHAFT, A DRIVING DISK ROTATABLE BY THE DRIVING SHAFT, AND A CLUTCH ASSEMBLY ROTATABLE BY THE DRIVING DISK. TWO PARALLEL GUIDING SLOTS ARE PROVIDED ON THE DRIVING SHAFT. AN ECCENTRIC PLATE WITH A NOTCH IS SLEEVED ONTO THE DRIVING SHAFT. A COMPRESSIBLE RESILIENT REGULATION MECHANISM IS DISPOSED BETWEEN THE NOTCH AND THE DRIVING SHAFT. THE DRIVING DISK IS INSTALLED ON THE ECCENTRIC PLATE VIA A BEARING. THE ECCENTRIC PLATE OFFSETS IN RELATION TO THE AXIS OF THE DRIVING SHAFT, AND AT THE SAME TIME THE ECCENTRIC PLATE DRIVES THE DRIVING DISK OFFSET. THE AUTOMATIC STEPLESS TRANSMISSION CAN COMPRESS OR RELEASE THE RESILIENT REGULATION MECHANISM ACCORDING TO LOADS. THE ECCENTRICITY BETWEEN THE ECCENTRIC PLATE AND THE DRIVING SHAFT CAN THEREFORE BE ADJUSTED, AND THE ECCENTRIC PLATE CAN DRIVE THE DRIVING DISK TO MOVE. THUS, THE ECCENTRICITY OF THE DRIVING DISK CAN BE REGULATED WITHOUT MANUAL WORK. THE TRANSMISSION HAS A SIMPLE STRUCTURE AND CAN BE OPERATED EASILY. IT CAN ADJUST THE TRANSMISSION RATIO AUTOMATICALLY. THEREFORE THE COST AND THE FAILURE RATE CAN BE REDUCED EFFICIENTLY.

CLAIMS:

1. AN AUTOMATIC STEPLESS TRANSMISSION COMPRISING:A DRIVE SHAFT, A DRIVE DISK DRIVEN BY THE DRIVE SHAFT, A CLUTCH WHEEL ASSEMBLY DRIVEN BY THE DRIVE DISK, AN OUTER SURFACE OF THE DRIVE SHAFT BEING PROVIDED WITH TWO PARALLEL GUIDE SLOTS, THE DRIVE SHAFT BEING RECEIVED IN A NOTCH OF AN ECCENTRIC PLATE AT THE POSITION OF THE GUIDE SLOTS, THE NOTCH OF THE ECCENTRIC PLATE DEFINING PARALLEL SEGMENTS ABUTTING AGAINST THE GUIDE SLOTS AND ALLOWING THE ECCENTRIC PLATE TO MOVE ONLY PARALLEL TO THE GUIDE SLOTS, A COMPRESSIBLE RESILIENT REGULATION MECHANISM DISPOSED BETWEEN AN INNER SIDE OF THE ECCENTRIC PLATE AND AN OUTER SURFACE OF THE DRIVE SHAFT, THE DRIVE DISK BEING MOUNTED ON THE ECCENTRIC PLATE THROUGH A BEARING, WHEREBY THE ECCENTRIC PLATE CARRIES OUT ECCENTRIC MOTION VERTICALLY TOWARDS THE AXIS OF THE DRIVE SHAFT UNDER THE REGULATION OF THE RESILIENT REGULATION MECHANISM, AND DRIVES THE DRIVE DISK TO CARRY OUT CORRESPONDING ECCENTRIC MOTION.

2. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 1, WHEREIN THE NOTCH OF THE ECCENTRIC PLATE FURTHER DEFINES AN ARC SEGMENT EXTENDING BETWEEN THE ENDS OF THE PARALLEL SEGMENTS FOR MATING WITH THE OUTER SURFACE OF THE DRIVE SHAFT.

3. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 1, WHEREIN THE RESILIENT REGULATION MECHANISM IS IN THE FORM OF A SPRING OR RUBBER DISPOSED BETWEEN AN INNER SIDE OF THE ECCENTRIC PLATE AND AN OUTER SURFACE OF THE DRIVE SHAFT.

4. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 3, WHEREIN THE INNER SIDE OF THE ECCENTRIC PLATE IS PROVIDED WITH A FIRST RECESS, THE DRIVE SHAFT IS PROVIDED WITH A SECOND RECESS OPPOSITELY FACING THE FIRST RECESS, AND THE SPRING OR RUBBER IS RECEIVED IN THE FIRST AND SECOND RECESSES.


5. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 1, WHEREIN THE RESILIENT REGULATION MECHANISM IS IN THE FORM OF A CHAMBER PROVIDED ON THE DRIVE SHAFT, AND A PISTON CONNECTED TO THE ECCENTRIC PLATE, AND THE CHAMBER IS FILLED WITH GAS OR LIQUID UNDER A PREDETERMINED PRESSURE.

6. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 1, WHEREIN THE RESILIENT REGULATION MECHANISM IS IN THE FORM OF A CHAMBER PROVIDED ON THE ECCENTRIC PLATE, AND A PISTON CONNECTED TO THE DRIVE SHAFT, AND THE CHAMBER IS FILLED WITH GAS OR LIQUID UNDER A PREDETERMINED PRESSURE.


7. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 1, WHEREIN THE MAXIMUM ECCENTRICITY OF THE DRIVE DISK IS HALF THE DIFFERENCE OF THE INNER DIAMETER OF THE BEARING AND THE DIAMETER OF THE DRIVE SHAFT.

8. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 7, WHEREIN THE MINIMUM ECCENTRICITY OF THE DRIVE DISK IS THE THICKNESS OF THE ECCENTRIC PLATE AT A CENTRAL LINE PARALLEL TO THE GUIDE SLOTS.


9. AN AUTOMATIC STEPLESS TRANSMISSION COMPRISING:A DRIVE SHAFT HAVING TWO PARALLEL GUIDE SLOTS;AN ECCENTRIC PLATE HAVING A NOTCH DEFINING TWO PARALLEL SEGMENTS SLIDABLY ENGAGED WITH THE TWO GUIDE SLOTS; ANDA COMPRESSIBLE RESILIENT REGULATION MECHANISM BEING DISPOSED BETWEEN THE DRIVE SHAFT AND THE ECCENTRIC PLATE;WHEREIN THE ECCENTRIC PLATE IS ADAPTED TO CARRY OUT ECCENTRIC MOTION BETWEEN A MINIMUM ECCENTRIC POSITION AND A MAXIMUM ECCENTRIC POSITION IN RESPONSE TO A LOAD ACTING ON THE RESILIENT REGULATION MECHANISM, THEREBY TRANSMITTING THE ECCENTRIC MOTION TO A DRIVE DISK MOUNTED ON THE ECCENTRIC PLATE THROUGH A BEARING.

10. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 9, WHEREIN THE ECCENTRIC PLATE HAS AN ARC SEGMENT EXTENDING BETWEEN THE ENDS OF THE TWO PARALLEL SEGMENTS, AND IS ADAPTED TO MATE WITH AND ABUT AGAINST AN OUTER SURFACE OF THE DRIVE SHAFT.

11. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 9, WHEREIN THE RESILIENT REGULATION MECHANISM IS IN THE FORM OF A SPRING.

12. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 9, WHEREIN THE RESILIENT REGULATION MECHANISM IS IN THE FORM OF A RUBBER.

13. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 9, WHEREIN THE RESILIENT REGULATION MECHANISM IS IN THE FORM OF A SPRING PLATE.

14. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 9, WHEREIN ONE END OF THE RESILIENT REGULATION MECHANISM IS RECEIVED IN A FIRST RECESS PROVIDED ON THE DRIVE SHAFT, AND THE OTHER END OF THE RESILIENT REGULATION MECHANISM IS RECEIVED IN A SECOND RECESS PROVIDED ON THE ECCENTRIC PLATE OPPOSITELY FACING THE FIRST RECESS.

15. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 9, WHEREIN THE RESILIENT REGULATION MECHANISM IS IN THE FORM OF A CHAMBER PROVIDED ON THE DRIVE SHAFT, AND A PISTON CONNECTED TO THE ECCENTRIC PLATE, AND THE PISTON IS SLIDABLE WITHIN THE CHAMBER WHICH IS FILLED WITH GAS OR LIQUID UNDER A PREDETERMINED PRESSURE.

16. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 9, WHEREIN THE RESILIENT REGULATION MECHANISM IS IN THE FORM OF A CHAMBER PROVIDED ON THE ECCENTRIC PLATE, AND A PISTON CONNECTED TO THE DRIVE SHAFT, AND THE PISTON IS SLIDABLE WITHIN THE CHAMBER WHICH IS FILLED WITH GAS OR LIQUID UNDER A PREDETERMINED PRESSURE.

17. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 9, WHEREIN THE ECCENTRIC PLATE IS GENERALLY C-SHAPED.

18. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 9, WHEREIN THE MAXIMUM ECCENTRICITY OF THE DRIVE DISK IS HALF THE DIFFERENCE OF THE INNER DIAMETER OF THE BEARING AND THE DIAMETER OF THE DRIVE SHAFT.

19. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 9, WHEREIN THE MINIMUM ECCENTRICITY OF THE DRIVE DISK IS THE THICKNESS OF THE ECCENTRIC PLATE AT A CENTER LINE PARALLEL TO THE GUIDE SLOTS.

20. THE AUTOMATIC STEPLESS TRANSMISSION AS CLAIMED IN CLAIM 9, FURTHER COMPRISING A CLUTCH WHEEL ASSEMBLY DRIVEN BY THE DRIVE DISK.

SPINDLE SERIES;

ARITHMETIC AND GEOMETRIC PROGRESSIONS

INTRODUCTION

ARITHMETIC AND GEOMETRIC PROGRESSIONS ARE PARTICULAR TYPES OF SEQUENCES OF NUMBERS WHICH OCCUR FREQUENTLY IN BUSINESS CALCULATIONS. THIS LEAFLET EXPLAINS THESE TERMS AND SHOWS HOW THE SUMS OF THESE SEQUENCES CAN BE FOUND.

ARITHMETIC PROGRESSIONS

AN ARITHMETIC PROGRESSION IS A SEQUENCE OF NUMBERS WHERE EACH NEW TERM AFTER THE FIRST IS FORMED BY ADDING A FIXED AMOUNT CALLED THE COMMON DIFFERENCE TO THE PREVIOUS TERM IN THE SEQUENCE. FOR EXAMPLE THE SEQUENCE

3, 5, 7, 9, 11...

IS AN ARITHMETIC PROGRESSION. NOTE THAT HAVING CHOSEN THE FIRST TERM TO BE 3, EACH NEW TERM IS FOUND

BY ADDING 2 TO THE PREVIOUS TERM, SO THE COMMON DIFFERENCE IS 2. THE COMMON DIFFERENCE CAN BE NEGATIVE: FOR EXAMPLE THE SEQUENCE

2, −1, −4, −7...

IS AN ARITHMETIC PROGRESSION WITH FIRST TERM 2 AND COMMON DIFFERENCE −3.

IN GENERAL WE CAN WRITE AN ARITHMETIC PROGRESSION AS FOLLOWS:

ARITHMETIC PROGRESSION: A, A + D, A + 2D, A + 3D, ...

WHERE THE FIRST TERM IS A AND THE COMMON DIFFERENCE IS D. SOME IMPORTANT RESULTS CONCERNING

ARITHMETIC PROGRESSIONS (A.P.) NOW FOLLOW:

THE NTH TERM OF AN A.P. IS GIVEN BY: A + (N − 1)D


THE SUM OF THE FIRST N TERMS OF AN A.P. IS SN = N(2A+(N-1)D) / 2

THE SUM OF THE TERMS OF AN ARITHMETIC PROGRESSION IS KNOWN AS AN ARITHMETIC SERIES.

GEOMETRIC PROGRESSIONS

A GEOMETRIC PROGRESSION IS A SEQUENCE OF NUMBERS WHERE EACH TERM AFTER THE FIRST IS FOUND BY

MULTIPLYING THE PREVIOUS TERM BY A FIXED NUMBER CALLED THE COMMON RATIO. THE SEQUENCE

1, 3, 9, 27 . . .

IS A GEOMETRIC PROGRESSION WITH FIRST TERM 1 AND COMMON RATIO 3. THE COMMON RATIO COULD BE A

FRACTION AND IT MIGHT BE NEGATIVE. FOR EXAMPLE, THE GEOMETRIC PROGRESSION WITH FIRST TERM 2 AND

COMMON RATIO −1

3 IS

2, −

2

3

,

2

9

,−

2

27

, . . .

IN GENERAL WE CAN WRITE A GEOMETRIC PROGRESSION AS FOLLOWS:

GEOMETRIC PROGRESSION: A, AR, AR2, AR3...

WHERE THE FIRST TERM IS A AND THE COMMON RATIO IS R.

SOME IMPORTANT RESULTS CONCERNING GEOMETRIC PROGRESSIONS (G.P.) NOW FOLLOW:

THE NTH TERM OF A G.P. IS GIVEN BY: AR (N1)

THE SUM OF THE FIRST N TERMS OF A G.P. IS SN =

A (1 − RN)

1 − R

(VALID ONLY IF R _= 1)

THE SUM OF THE TERMS OF A GEOMETRIC PROGRESSION IS KNOWN AS A GEOMETRIC SERIES.

IF THE COMMON RATIO IN A GEOMETRIC SERIES IS LESS THAN 1 IN MODULUS, (THAT IS −1 < R < 1), THE SUM OF AN INFINITE NUMBER OF TERMS CAN BE FOUND. THIS IS KNOWN AS THE SUM TO INFINITY, S.

S =

A

1 − R

PROVIDED − 1 < R < 1

EXERCISES

1. FIND THE 23RD TERM OF AN A.P. WITH FIRST TERM 2 AND COMMON DIFFERENCE 7.

2. A G.P. IS GIVEN BY 1, 1

2, 1

4 . . . WHAT IS ITS COMMON RATIO?

3. FIND THE 7TH TERM OF A G.P. WITH FIRST TERM 2 AND COMMON RATIO 3.

4. FIND THE SUM OF THE FIRST FIVE TERMS OF THE A.P. WITH FIRST TERM 3 AND COMMON DIFFERENCE 5.

5. FIND THE SUM OF THE FIRST FIVE TERMS OF THE G.P. WITH FIRST TERM 3 AND COMMON RATIO 2.

6. FIND THE SUM OF THE INFINITE GEOMETRIC SERIES WITH FIRST TERM 2 AND COMMON RATIO 1

2 .

ANSWERS

1. 156, 2. 1

2 , 3. 1458, 4. 65, 5. 93, 6. 4.

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