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Treadmill deceleration system and method    
United States Patent5489250   
Link to this pagehttp://www.wikipatents.com/5489250.html
Inventor(s)Densmore; Bruce D. (Seattle, WA); Hass; Lester A. (Duvall, WA); Rotunda; John T. (Renton, WA); Fissel; Gregory W. (Seattle, WA)
AbstractA high speed deceleration device and method is disclosed that operates on a D.C. speed-change motor used to change the transmission configurations on the transmission of a treadmill powered by a constant speed drive motor. In ordinary use, normal transmission acceleration and deceleration rates are used to speed up or slow down the treadmill belt. A deceleration control signal causes a high voltage to be provided to the D.C. speed-change motor. The high voltage causes the D.C. speed-change motor to rapidly change the transmission configurations on the treadmill which causes a rapid deceleration of the treadmill belt. The deceleration control signal is produced in response to a user direction or in response to the condition of the treadmill. Once the belt has been slowed below a threshold speed, the machine shuts itself off. During the deceleration process, the drive motor of the treadmill continues to provide power to the treadmill belt through the transmission so that the transmission continues to move during the deceleration process.
   














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Drawing from US Patent 5489250
Treadmill deceleration system and method - US Patent 5489250 Drawing
Treadmill deceleration system and method
Inventor     Densmore; Bruce D. (Seattle, WA); Hass; Lester A. (Duvall, WA); Rotunda; John T. (Renton, WA); Fissel; Gregory W. (Seattle, WA)
Owner/Assignee     Quinton Instrument Company (Bothell, WA)
Patent assignment
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Publication Date     February 6, 1996
Application Number     08/201,870
PAIR File History     Application Data   Transaction History
Image File Wrapper   Patent Term   Fees
Litigation
Filing Date     February 25, 1994
US Classification     482/54 482/7 482/901
Int'l Classification     A63B 022/02 A63B 024/00
Examiner     Apley; Richard J.
Assistant Examiner     Leubecker; John P.
Attorney/Law Firm     Beck; Andrew J. Smith; Montgomery W. , Allison; Richard D. ,
Address
Parent Case     This application is a division of application Ser. No. 790,750, filed Nov. 8, 1991, now U.S. Pat. No. 5,290,205, issued Mar. 1, 1994.
Priority Data    
USPTO Field of Search     482/1 482/4 482/7 482/9 482/54 482/901 198/577 198/794
Patent Tags     treadmill deceleration
   
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Dalebout

Nov,1991

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4964841
Takayama
474/11
Oct,1990

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Salerno
474/11
Jul,1990

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Sabin
482/80
May,1990

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Sweeney, Sr.
482/54
Jun,1989

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4792134
Chen
482/54
Dec,1988

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4749181
Pittaway
482/7
Jun,1988

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Shu
482/7
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Krukowski
601/26
Dec,1986

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Otte
482/4
Dec,1982

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Van Doren
318/252
Apr,1977

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Moody
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Oct,1976

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O'Berto
474/11
May,1976

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Oscar M Hagen, 116 S. 23rd St. (La Crosse, WI 54601)
482/54
Sep,1972

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We claim:

1. A method for rapidly decelerating a treadmill belt in a treadmill having a constant speed drive motor with a rotating member, a treadmill belt, a transmission for connecting the rotating member to the treadmill belt causing the treadmill belt to move in response to rotation of the rotating member, a D.C. speed change motor for varying the internal configurations of the transmission to vary the speed of the treadmill belt when the rotating member is rotating at a generally constant speed, the D.C. speed change motor, in normal operation, responding to voltage applied within a specified range of voltages, the method comprising the steps of:

producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated;

producing a D.C. deceleration voltage of a voltage larger than the specified range of voltages normally applied to the D.C. speed change motor;

applying the D.C. deceleration voltage to the D.C. speed change motor in response to said rapid deceleration control signal, thereby causing the D.C. speed change motor to rapidly vary the internal configurations of the transmission;

whereby, the speed of the treadmill belt is rapidly decelerated.

2. The method of claim 1 wherein said step of producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated includes the step of determining that the power to the treadmill has been interrupted and then restored.

3. The method of claim 1 wherein said step of producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated includes the step of determining whether the treadmill user has indicated that the user would like to immediately stop the treadmill belt.

4. The method of claim 1 wherein said step of producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated includes the step of sensing the occurrence of a drive motor overload condition.

5. The method of claim 1 wherein said step of producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated includes the steps of:

timing the time that a voltage larger than the specified range of voltages normally applied to the D,C, speed change motor has been applied to the D.C. speed change motor;

determining that the time that a voltage larger than the specified range of voltages normally applied to the D,C, speed change motor has been applied to the D,C, speed change motor exceeds a preset time period.

6. The method of claim 1 further comprising the step of:

sensing the speed of the treadmill belt;

turning off the drive motor once the sensed speed of the treadmill belt drops below a predetermined speed.

7. The method of claim 6 wherein said step of producing a rapid deceleration control signal includes the step of determining that the speed of the treadmill belt exceeds a predetermined speed.

8. The method of claim 6 wherein said step of producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated includes the step of determining that the power to the treadmill has been interrupted and then restored.

9. The method of claim 6 wherein said step of producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated includes the step of determining whether the treadmill user has indicated that the user would like to immediately stop the treadmill belt.

10. The method of claim 6 wherein said step of producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated includes the step of sensing the occurrence of a drive motor overload condition.

11. The method of claim 6 wherein said step of producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated includes the steps of:

timing the time that a voltage larger than the specified range of voltages normally applied to the D.C. speed change motor has been applied to the D.C. speed change motor;

determining that the time that a voltage larger than the specified range of voltages normally applied to the D.C. speed change motor has been applied to the D.C. speed change motor exceeds a preset time period.

12. A method for causing the rapid deceleration of a treadmill belt in a treadmill having an A.C. drive motor with a rotating member, a treadmill belt, a transmission for connecting the rotating member to the treadmill belt so that rotation of the rotating member causes the treadmill belt to move and a D.C. speed change motor for varying the internal configurations of the transmission to vary the speed of the treadmill belt when the rotating member is rotating at a generally constant speed, the D.C. speed change motor, in normal operation, responding to voltage applied within a specified range of voltages, comprising the steps of:

sensing the speed of the treadmill belt;

producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated;

producing a D.C. deceleration voltage of a voltage larger than the specified range of voltages normally applied to the D.C. speed change motor;

applying the D.C. deceleration voltage to the D.C. speed change motor in response to a determination that the speed of the treadmill belt is above a threshold speed and in response to said rapid deceleration control signal, thereby causing the D.C. speed change motor to rapidly vary the internal configurations of the transmission;

whereby, the speed of the treadmill belt is rapidly decelerated.

13. The method of claim 12 wherein said step of producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated includes the step of determining that the power to the treadmill has been interrupted and then restored.

14. The method of claim 12 wherein said step of producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated includes the step of determining whether the treadmill user has indicated that the user would like to immediately stop the treadmill belt.

15. The method of claim 12 wherein said step of producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated includes the step of sensing the occurrence of a drive motor overload condition.

16. The method of claim 12 wherein said step of producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated includes the steps of:

timing the time that a voltage larger than the specified range of voltages normally applied to the D.C. speed change motor has been applied to the D.C. speed change motor;

determining that the time that a voltage larger than the specified range of voltages normally applied to the D.C. speed change motor has been applied to the D.C. speed change motor exceeds a preset time period.

17. The method of claim 12 further comprising the step of turning off the drive motor once the sensed speed of the treadmill belt drops below a predetermined speed.

18. A method for causing the rapid deceleration of a treadmill belt in a treadmill having an A.C. drive motor with a rotating member, a treadmill belt, a transmission for connecting the rotating member to the treadmill belt so that rotation of the rotating member causes the treadmill belt to move and a D.C. speed change motor for varying the internal configurations of the transmission to vary the speed of the treadmill belt when the rotating member is rotating at a generally constant speed, the D.C. speed change motor, in normal operation, responding to voltage applied within a specified range of voltages, comprising the steps of:

producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated;

sensing the speed of the treadmill belt;

producing a voltage proportional to the sensed speed of the treadmill belt;

producing a threshold voltage level representative of a predetermined threshold speed of the treadmill belt;

comparing the voltage representative of the speed of the treadmill belt to said threshold voltage level;

producing a speed determination signal if the voltage representative of the sensed speed of the treadmill belt is above said threshold voltage, said speed determination signal indicating that the speed of the treadmill belt is above said threshold speed;

producing a D.C. deceleration voltage of a voltage larger than the specified range of voltages normally applied to the D.C. speed change motor;

applying said D.C. deceleration voltage to the D.C. speed change motor in response to the presence of both said speed determination signal and said rapid deceleration control signal, thereby causing the D.C. speed charge motor to rapidly vary the internal configurations of the transmission;

whereby, the speed of the treadmill belt is rapidly decelerated.

19. The method of claim 18 wherein said step of producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated includes the step of determining that the power to the treadmill has been interrupted and then restored.

20. The method of claim 18 wherein said step of producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated includes the step of determining whether the treadmill user has indicated that the user would like to immediately stop the treadmill belt.

21. The method of claim 18 wherein said step of producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated includes the step of sensing the occurrence of a drive motor overload condition.

22. The method of claim 18 wherein said step of producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated includes the steps of:

timing the time that a voltage larger than the specified range of voltages normally applied to the D.C. speed change motor has been applied to the D.C. speed change motor;

determining that the time that a voltage larger than the specified range of voltages normally applied to the D.C. speed change motor has been applied to the D.C. speed change motor exceeds a preset time period.

23. A method for rapidly decelerating and stopping a treadmill belt in a treadmill having an A.C. drive motor with a rotating member, a treadmill belt, a transmission for connecting the rotating member to the treadmill belt causing the treadmill belt to move in response to rotation of the rotating member, a D.C. speed change motor for varying the internal configurations of the transmission to vary the speed of the treadmill belt when the rotating member is rotating at a generally constant speed, the D.C. speed change motor, in normal operation, responding to voltage applied within a specified range of voltages, and a rapid deceleration control signal indicating that the treadmill belt should be decelerated, comprising the steps of:

producing a D.C. deceleration voltage of a voltage larger than the specified range of voltages normally applied to the D.C. speed change motor;

applying the D.C. deceleration voltage to the D.C. speed change motor in response to the rapid deceleration control signal, thereby causing the D.C. speed change motor to rapidly vary the internal configurations of the transmission;

applying electrical power to the A.C. drive motor until the speed of the treadmill belt is below a threshold speed;

terminating the application of electrical power to the A.C. drive motor after the speed of the treadmill belt has been slowed below the threshold speed;

whereby, the speed of the treadmill belt is rapidly decelerated to the threshold speed whereafter the movement of the treadmill belt is terminated.

24. The combination of a device for rapidly decelerating a treadmill belt and a treadmill having a constant speed drive motor with a rotating member, a treadmill belt, a transmission for connecting the rotating member to the treadmill belt causing the treadmill belt to move in response to rotation of the rotating member, a D.C. speed change motor for varying the internal configurations of the transmission to vary the speed of the treadmill belt when the rotating member is rotating at a generally constant speed, the D.C. speed change motor, in normal operation, responding to voltage applied within a predetermined range of voltages, the device comprising:

a rapid deceleration control signal producing member to indicate that said treadmill belt should be decelerated;

a D.C. deceleration voltage producing member for producing a voltage larger than said predetermined range of voltages normally applied to said D.C. speed change motor;

a D.C. deceleration voltage application member for applying said D.C. deceleration voltage to said D.C. speed change motor in response to said rapid deceleration control signal, thereby causing said D.C. speed change motor to rapidly vary said internal configurations of the transmission;

whereby, the speed of said treadmill belt is rapidly decelerated.

25. The combination of a device for rapidly deceleratinq a treadmill belt and a treadmill having a constant speed drive motor with a rotating member, a treadmill belt, a transmission for connecting the rotating member to the treadmill belt causing the treadmill belt to move in response to rotation of the rotating member, a D.C. speed change motor for varying the internal configurations of the transmission to vary the speed of the treadmill belt when the rotating member is rotating at a generally constant speed, the D.C. speed change motor, in normal operation, responding to voltage applied within a predetermined range of voltages, the device comprising:

a micro-controller for producing a rapid deceleration control signal indicating that said treadmill belt should be decelerated;

a high speed deceleration voltage supply member for producing a D.C. deceleration voltage which is a voltage larger than said predetermined range of voltages normally applied to said D.C. speed change motor;

a relay member for applying said D.C. deceleration voltage to said D.C. speed change motor in response to said rapid deceleration control signal, thereby causing said D.C. speed change motor to rapidly vary said internal configurations of the transmission;

whereby, the speed of said treadmill belt is rapidly decelerated.

26. The device of claim 25 further comprising a determining member for determining that the power to said treadmill has been interrupted and then restored.

27. The device of claim 25 further comprising a determining member for determining whether the treadmill user has indicated that the user would like to immediately stop said treadmill belt.

28. The device of claim 25 further comprising a sensing member for sensing the occurrence of a drive motor overload condition.

29. The device of claim 25 further comprising: a timer for timing the time that said voltage larger than predetermined range of voltages normally applied to said D.C. speed change motor has been applied to said D.C. speed change motor by said high speed deceleration voltage supply means; and,

a determining member for determining that said timer has timed a time that exceeds a preset time period.

30. The device of claim 25 further comprising:

a sensing member for sensing the speed of said treadmill belt;

a shut off member for turning off said drive motor once the sensed speed of said treadmill belt drops below a predetermined speed.

31. The device of claim 30 wherein said sensing member includes an optical tachometer attached to said transmission.

32. The device of claim 31 wherein said sensing member further includes a tachometer frequency to voltage converter having an input for receiving signals from said optical tachometer, said tachometer frequency to voltage converter receiving signals from said optical tachometer.

33. The device of claim 32 wherein said tachometer frequency to voltage converter includes:

a frequency doubler;

a filter connected to said frequency doubler for filtering the output of said frequency doubler to produce a D.C. filtered voltage which is inversely proportional to the frequency of the signal output from said frequency doubler;

whereby the filtered voltage produced by said filter is inversely proportional to the speed of said treadmill belt;

a threshold voltage level producing member for producing a threshold voltage level representative of a predetermined threshold speed of said treadmill belt;

a comparison member for comparing the filtered voltage produced by said filter to the threshold voltage level and for producing a speed determination signal if the filtered voltage is below the threshold voltage, said speed determination signal connected to said relay member, said speed determination signal indicating that the speed of said treadmill belt is above a threshold speed.

34. The device of claim 30 wherein said device further comprises a member for applying said D.C. deceleration voltage to said D.C. speed change motor including a software high speed deceleration command module connected to said sensing member and to said rapid deceleration control signal, said command module producing a control signal if said treadmill belt is running at a speed above the desired threshold and said rapid deceleration control signal indicates that a rapid deceleration is desired;

wherein said relay member is connected to said command module and is enabled in response to said control signal and connects said high speed deceleration voltage supply member to said D.C. speed change motor.

35. The device of claim 30 wherein said device includes a determining member for determining that the sensed speed of said treadmill belt exceeds a predetermined speed.

36. The device of claim 30 wherein said device further comprises a determining member for determining that the power to said treadmill has been interrupted and then restored.

37. The device of claim 30 wherein said device further comprises a determining member for determining whether the treadmill user has indicated that the user would like to immediately stop said treadmill belt.

38. The device of claim 30 wherein said device further comprises a sensing member for sensing the occurrence of an overload condition of said drive motor.

39. The device of claim 30 wherein said device further comprises:

a timer for timing the time that said voltage larger than said predetermined range of voltages which is normally applied to said D.C. speed change motor has been applied to said D.C. speed change motor by said high speed deceleration voltage supply member; and

determining member for determining that said timer has timed a time that exceeds a preset time period.

40. The combination of a device for rapidly decelerating a treadmill belt and a treadmill having a constant speed drive motor with a rotating member, a treadmill belt, a transmission for connecting the rotating member to the treadmill belt causing the treadmill belt to move in response to rotation of the rotating member, a D.C. speed change motor for varying the internal configurations of the transmission to vary the speed of the treadmill belt when the rotating member is rotating at a generally constant speed, the D.C. speed change motor, in normal operation, responding to voltage applied within a predetermined range of voltages, the device comprising:

a) high speed deceleration voltage supply member for producing a D.C. deceleration voltage of a voltage larger than said predetermined range of voltages normally applied to said D.C. speed change motor;

b) a first determining member for determining that the power to said treadmill has been interrupted and then restored;

c) a second determining member for determining whether the treadmill user has indicated that the user would like to immediately stop said treadmill belt;

d) a first sensing member for determining that the occurrence of an overload condition of said drive motor;

e) a timer for timing the time that a voltage larger than the specified range of voltages normally applied to the D.C. speed change motor has been applied to the D.C. speed change motor by said high speed deceleration voltage supply means;

f) a third determining member for determining that said timer has timed a time that exceeds a preset time period;

g) a micro-controller for producing a rapid deceleration control signal indicating that the treadmill belt should be decelerated in response to:

1) said first determining member;

2) said second determining member;

3) said first member; or

4) said timer;

h) relay member for applying said D.C. deceleration voltage to said D.C. speed change motor in response to said rapid deceleration control signal, thereby causing said D.C. speed change motor to rapidly vary said internal configurations of the transmission;

i) a second sensing member for sensing the speed of said treadmill belt;

j) a shut off member for turning off said drive motor once the sensed speed of said treadmill belt drops below a predetermined speed;

whereby, the speed of said treadmill belt is rapidly decelerated.
 Description Submit all comments and votes
 


A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a method and system for rapidly decelerating a treadmill belt and more specifically relates to a method and system for rapidly decelerating a treadmill belt on a treadmill having a D.C. motor that changes the internal configurations of a transmission on a treadmill powered by a constant speed drive motor, which transmission connects the constant speed drive motor to the belt of the treadmill.

2. Description of Related Art

Treadmills require a drive motor to provide power to the treadmill's belt. Most often, these drive motors are AC motors which turn at only one speed which speed depends on the frequency of the AC power supply. In order to provide various speeds for the treadmill belt, these AC drive motors are connected to the treadmill belt through a mechanical transmission which changes its internal configuration to provide the various speeds for the treadmill belt. The internal configurations of the mechanical transmission is typically set by a relatively small speed-change motor. As the speed-change motor turns, the transmission's internal configuration changes so that the treadmill belt speed either increases or decreases depending on the direction that the speed-change motor is turning.

Referring to FIG. 1, a typical treadmill transmission, generally labelled 1, is shown. Typically, these transmissions have a pair of adjustable pulleys 4,7 connected by a transmission belt 6. A first pulley 4 is connected to a drive motor 2 through an input shaft 3 so that rotation of the drive motor 2 rotates this first pulley 4. This first pulley 4 has two opposing conical plates 5a,b which form a V-shape for frictionally receiving a correspondingly shaped transmission belt 6.

The transmission 1 also has a second pulley 7. The second pulley 7 has a set of opposed conical plates attached to an output shaft 9. The conical plates 8a,b of the second pulley 7 also form a V-shaped recess for frictionally receiving the transmission belt 6 therebetween. The output shaft 9 is in turn attached to a drive roller 11 through a drive belt 10. Rotation of the drive roller 11 causes the treadmill belt (not shown) to move.

Typically in such a transmission 1, a speed-change motor 12 moves the two plates 5a,b of the first pulley 4 either closer together or further apart. Because of the conical shape of the opposed plates 5a,b, as the plates are moved further apart and tension is placed on the transmission belt 6, the transmission belt 6 situated around the first pulley 4 will move closer to the center of the input shaft 3. As the two plates 5a,b are moved closer together by the speed-change motor 12, the transmission belt 6 is moved more towards the outer edge of the first pulley 4.

The plates 8a,b of the second pulley 7 are biased in a position toward each other by a tension spring 13. However, sufficient pressure by the transmission belt 6 on the conical plates 8a,b of the second pulley 7 will overcome the inherent bias of the plates to be together and force them apart thereby allowing the transmission belt 6, which is under tension, to move from a position more towards the outer edge of the plates 8a,b to a position closer towards the output shaft 9. In this way the mechanical advantage imparted to the drive roller 11, and subsequently to the treadmill belt from the drive motor 2, changes depending on the position of the transmission belt 6 on the first and second pulleys 4,7.

The rate of change of the speed of the treadmill belt is dependent on both the current speed of the treadmill belt, that is, on the current position of the transmission belt 6 on pulleys 4,7, and on how fast the speed-change motor 12 is turning.

Previous transmissions have used AC speed-change motors. However, under normal operating conditions, AC motors turn at only one speed regardless of the current or voltage applied to the motor. Consequently, the speed at which the opposing conical plates 5a,b are moved together or apart as driven by the AC speed change motor is a constant. In a transmission using an AC speed-change motor, the entire change in the speed of the treadmill belt results from the change in position of the transmission belt 6 on pulleys 4,7 and not from any change in the rate that the conical plates 5a,b are moved together or apart. A constant rate of moving the conical plates 5a,b together or apart as a result of the constant speed of the AC speed change motor 12 results in a non-constant rate of change for the speed of the treadmill belt as illustrated in FIG. 2.

This non-constant rate of speed change has two primary sources. First, the belt connecting the pulleys has a constant length. As shown in FIG. 1, as the plates 5a,b of the first pulley 4 move together or apart in response to the rotation of the speed-change motor 12, the location of the transmission belt 6 on plates 5a,b changes. As the conical plates 5a,b move apart, the transmission belt 6 will have less tension on it. As a result of the reduction of tension on the transmission belt 6, the tension spring 13 will push plates 8a,b together thereby moving transmission belt 6 farther away from the output shaft 9. As transmission belt 6 moves away from output shaft 9, tension is placed on transmission belt 6 by tension spring 13 pulling it into snug frictional contact with conical plates 5a,b at a position closer to input shaft 3 than it had been prior to conical plates 5 a,b moving apart in response to the rotation of speed change motor 12. Transmission belt 6 will move out from output shaft 9 until the tension in transmission belt 6 equals the tension applied by tension spring 13. This causes the mechanical ratio of pulley 4 and pulley 7 to change. This relationship is illustrated in FIG. 3.

The exact equation for the transmission belt circumference is found by the sum of the straight portions (l+l) and the two partial circumferences (c.sub.1 +c.sub.2). This leads to the following equation:

Circumference=2d.multidot.sin .theta.+2.theta..multidot.r.sub.1 +2(.pi.-.theta..multidot.r.sub.2) 1)

where:

.theta.=cos.sup.-1 ((r.sub.2 -r.sub.1)/d), and .theta. is in radians;

r.sub.1 =the radius of the transmission belt 6 around first pulley 4;

r.sub.2 =the radius of the transmission-belt 6 around second pulley 7;

d=the distance between first pulley 4 and second pulley 7; and,

1=d.multidot.sin .theta.=((d.sup.2 -(r.sub.2 -r.sub.1).sup.2).sup.1/2.

This equation is extremely difficult to solve for r.sub.2 in terms of r.sub.1. Equation 1 can be simplified by making the following approximations:

c.sub.1 =.pi.r.sub.1

c.sub.2 =.pi.r.sub.2, and

l=((d.sup.2 -(r.sub.2 -r.sub.1).sup.2).sup.1/2 +.pi.(r.sub.2 +r.sub.1)

so that:

Circumference=2((d.sup.2 -(r.sub.2 -r.sub.1).sup.2).sup.1/2 +.pi.(r.sub.2 -r.sub.1) 2)

The error created in this approximation is very small and creates an equation which is more easily solved. Since Circumference is the circumference of transmission belt 6 which is a constant "C", and "d", the distance between pulleys 4 and 7, is a constant, the following quadratic equation is derived:

(.pi.-4)r.sub.2.sup.2 +((2.pi..sup.2 +8)r.sub.1 -2.pi.C)r.sub.2 +((.pi..sup.2 -4)r.sub.1.sup.2 -2.pi.Cr.sub.1 +C.sup.2 -4d.sup.2)=0.3)

Solving for r.sub.2 gives:

r.sub.2 =(.pi.C-(.pi..sup.2 +4)r.sub.1 .+-.2(4.pi..sup.2 r.sub.1.sup.2 -4.pi.Cr.sub.1 +C.sup.2 +d.sup.2 (.pi..sup.2 -4)).sup.1/2)/(.pi..sup.2 -4)4)

Realistic values show the ".+-." factor is subtracted, only, in this