GB2176283A - Gyroscopes - Google Patents

Abstract

It is known to measure the position or the angle of tilt of a body using the spinning rotor 1 of a gyroscope, the spherical surface of the rotor having a pattern of areas of differing reflectivities 3, 4. Optical pickoffs 9, 10 are mounted to project radiation onto the spherical surface and to receive radiation reflected back from it, the movement in rotor position being indicated by the signals received by the pickoffs. However, an output signal indicative of the rotor position requires complicated and costly processing electronics due to the complexity of the equations giving rotor position. Described herein is the spherical surface of a gyroscope having a boundary 5 between the differing reflectivities 3, 4 defined by an inverse sine function which simplifies the equations giving rotor position and hence reduces the complexity and cost of the electronic processing equipment required. <IMAGE>

Description

SPECIFICATION Gyroscopes This invention relates to gyroscopes and in particular to gyroscopes used with optical pick-offs for sensing position of a body.

It is known to use the spinning rotor of a gyroscope to measure the position or angle of tilt of a body. One such gyroscope is disclosed in our copending patent application no. 2149500.

The gyroscope disclosed in this application comprises a spinning rotor having a pattern of areas of differing reflectivities eg complementary triangles of relatively high and relatively low reflectivity over its spherical surface. In this case, two optical pick-offs are mounted on respective axes perpendicular to the axis of rotation of the spinning rotor, each pick-off being an emitter-receiver arrangement for projecting radiation onto the spherical surface and for receiving the radiation reflected back from the surface, so that any movement in position of the rotor can be measured relative to the two axes eg pitch and yaw. The pattern of complementary triangles on the spherical surface of the rotor is simple and it is easy to determine the mark-space ratio ie the ratio of high to low reflectivity, for each pick-off for a given rotor position.However, in order to obtain an output signal indicative of the rotor position complicated and costly processing electronics are required due to the complexity of the equations which give the rotor position.

It is therefore an object of the invention to provide a gyroscope in which simplified equations and hence simplified electronic processing can be used to determine rotor position.

According to a first aspect of the invention, there is provided a gyroscope comprising sensing means and a rotor having a surface defining at least part of a sphere including an equator of the sphere and portions to each side of the equator, said surface comprising a pattern of two or more areas having respective ones of two different values of a property to which the sensing means is responsive, and said rotor being able to spin about a spin axis which is perpendicular to the plane containing the equator and being able to tilt with respect to the sensing means about at least one axis perpendicular to the spin axis such that, in use, with the rotor spinning and with a given amount of tilt, the sensing means forms an electrical signal having alternately a mark and a space value indicative of the changes in the value of said property along a line of latitude around the surface, which line of latitude is at a latitude angle relative to the equator dependent upon the amount of tilt and being positive for latitudes to one side of the equator and negative for latitudes to the other side of the equator, the pattern being such that the markspace ratio P of the electrical signal is related to the latitude angle by the equation:

K(P-1) a=sin-1 # # P+1 The sensing means may comprise optoelectrical transducing means and the property of the surface to which the sensing means is responsive may be an optical property, for example the colour or reflectivity of the surface.

The gyroscope may comprise first and second sensors, each operable to provide an electrical signal indicative of the changes in value of the property along a line of latitude around the surface, the first and second sensors being positioned so that when the rotor is tilted relative to the sensing means about only one axis perpendicular to said spin axis, the first and second sensors from respective electrical signals indicative of the changes along the same line of latitude at one side of the equator and, when the rotor is tilted only about the othqr axis perpendicular to the spin axis, the first and second sensors form respective electrical signals indicative of the changes along respective lines of latitude equispaced but at respective opposite sides of the equator.

According to a second aspect of the present invention, there is provided a gyroscopic sensing system for measuring pitch and roll of a missile, the system comprising: a gyroscope rotor having a spherical surface respective parts of which have different values of optical reflectivity, the boundary between said parts being defined by an inverse sine function; first and second optical sensors for sensing the reflectivity of respective adjacent portions of said surface and thereby forming output signals indicative of the position of the rotor; and processing means for processing said output signals to provide said pitch and roll measurements.

Preferably, said inverse sine function relates the angle of longitude a and the angle of latitude a of a point on said boundary according to the equation

-2K# a=sin-1 # # # According to a third aspect of the invention, there is provided a gyroscopic sensing system comprising:: a rotor which spins about a spin axis and tilts about two further axes, each further axis being perpendicular to said spin axis and to one another, the rotor having a spherical surface on which is formed a pattern of differing reflectivity, the boundary between differing reflectivities being defined by an inverse sine function which relates the angles of latitude and longitude, a and , of each point on the boundary; first and second sensing means mounted at an angle S to one of said perpendicular axes and each being operable to form electrical output signals corresponding to respective mark-space ratios P, and P2 which are indicative of the reflectivity of the pattern along lines of latitude around the spherical surface; and processing means for processing said output signals to provide respective measurements of tilt, 0 and 0, about said two axes.

Advantageously said processing means comprises a microprocessor coupled to a programmable read-only memory (PROM), the microprocessor being operable for evaluating equations to determine said measurements of tilt using look-up values stored in the PROM, the equations being

K P1-1 P2-1 #=sin-1 # # + # # 2 cos S P1+1 P2+1 and K P2-1 P1-1 #=sin-1 # # - # # 2 sin S cos # P2+1 P1+1 For a better understanding of the invention, reference will now be made, by way of example, to the accompanying drawings in which:: Figure 1 is a side elevation of a gyroscope rotor having a reflective/non-reflective pattern on its spherical surface; Figure 2 is a plan view of the Fig. 1 rotor; Figure 3 is a sketch of a single pattern used on the Fig. 1 rotor; and Figure 4 is a sketch of a double pattern used on the Fig. 1 rotor.

The theory of a rotor pattern obeying an inverse sine relation (ie the latitude of any point on the pattern profile being proportional to the inverse sine of the longitude at that point measured from some arbitrary zero) has been developed. This form of pattern is shown to greatly reduce the computing effort involved in evaluating the equations that convert the mark-space ratio outputs from the pick-off systems into pitch and roll angles. This is a desirable situation since the method of computation likely to be imlemented is a microprocessor coupled to a PROM (Programmable Read Only Memory) and any development that will reduce computing time and/or the cost of the microprocessor unit is an obvious advantage.

The rotor 1 shown in Figs. 1 and 2 has a spherical surface on which a pattern 2 is formed.

The pattern 2 comprises areas of relatively low reflectivity 3 and relatively high reflectivity 4 which are separated by boundaries 5. The rotor 1 is mounted so that it spins about a spin axis 6 and is able to tilt about two further axes, pitch axis 7 and roll axis 8 which are orthogonal to each other and to the axis 6. Optical pick-offs 9 and 10 are mounted in the rotor case (not shown) and are operable for projecting radiation onto the spinning rotor surface and for receiving the radiation reflected back from the surface, producing output signals in accordance with the reflected radiation received. The pick-offs 9 and 10 are mounted so that they each make an angle of 45" with the roll axis 8 in the plane containing the pitch and roll planes, each pick-off comprising an emitter 11, 12 and a receiver 13, 14. The emitters 11, 12 are light-emitting diodes (LEDs) and the receivers 13, 14 are photo-transistors. In operation, each pick-offpro- duces pulsed output signals in accordance with the reflected radiation from the surface of the rotor 1.

The latitudes a' and ,B' of two points of light from the LEDs 11 and 12 moving across the spherical surface of the rotor 1 as the rotor is tilted due to angles or pitch 0 and roll H, can be shown to be: &alpha;;'-sin-1 (cos 45 sin #-sin 45 cos # sin #) (1) ss'=sin-' (cos 45 sin #+sin 45 cos (p sin #) (2) In order to obtain a solution to the above equations, let sin-1 (cos 45 sin (p-sin 45 cos # sin 0)=f(P,) (3) and sin-1 (cos 45 sin (p+sin 45 cos # sin 6)=f(P2) (4) where P, and P2 are mark-space ratios provided by pick-offs 9 and 10 respectively.

After solving (3) and (4),

sin (f(P,))+sin (f(P2)) #=sin-1 # # (5) V2 sin (f(P2))-sin (f(P1)) #=sin-1 # # (6) V2 cos # From (5) and (6) it can be seen that there is a function of P1 and P2 that will result in a simple relationship for both pitch and roll with respect to mark-space ratios, ie an inverse sine function of the form

K(P-1) a=sin-1 # # P+1 where K is a constant; a is the latitude and P is the mark-space ratio at that latitude. This form gives the following: (i) a=O when P= 1 (ii) a symmetrical pattern (iii) a reduction in processing complexity.

Therefore, for pick-off 9

K(P1-1) f(P1)=sin@1 # # (7) P1+1 and for pick-off 10,

K(P2-1) f(P2)=sin@1 # # (8) P2+1 substituting (7) and (8) in (5) and (6)

P1-1 P2-1 #=sin-1 # A # + # # (9) P1+1 P2+1 and

A P2-1 P1-1 #=sin-1 # # - # # (10) cos # P2+1 P1+1 where A=K/V2 The pulsed output signals from the pickoffs 9, 10 are fed to processing means (not shown) which processes the signals to form values representative of the resective mark-space ratios P1, P2 of the signals, and wherein the values of pitch # and roll 0 are calculated from these values in accordance with equations (9) and (10) above.The processing means may comprise a micropro cessor-based computer system which, in dependence, upon P, and P2 accesses values of # and 6 pre-stored in a look-up table implemented, for example, by a programmable read only memory (PROM).

Change in latitude can be thought of as a measure of movement due to either pitch or roll depending on the mounting of the rotor, and if measurement of movement in both directions is required ie angular displacement, longitude will have to be included. A convenient way of representing P in terms of displacement from zero to the longitude pattern edge at a given latitude is #-2# P= (11) #+2# where a is the longitude at the pattern edge.

As the profile ie the boundary, an inverse sine law:

K(P-1) a=sin-1 # # P+1

-2K# -sin@1 # # (12) # Equation (12) relates the angles of longitude and latitude to each other at points on the boundary of the light and dark ie reflective and non-reflective portions of the pattern.Therefore, the boundaries 5 are defined by the equation

-2K# a=sin-1 # # # where a is the latitude of any point on the boundary; J is the longitude of the same point on the boundary; and K is a constant.

The maximum angle of latitude may be calculated from equations (1) and (2) if the maximum angles of pitch and roll, # and 6 respectively, for a given rotor are known. For example, for a maximum pitch and roll angle of 40 , equations (1) and (2) give a'=6.104 and ss'=53.388 respectively. As ss' > a', the maximum latitude is 53.388 . Similarly, by substituting a pitch and roll angle of 400, a minimum latitude of 53.3880 is obtained. As can be seen from Fig. 3, the pattern has rotational symmetry about an axis 15 through the line representing 0 latitude, with the boundary 5 between low and high reflectivities 3 and 4 shown.

Equation (11) limits the maximum value of a to #/2 ie #max=#/2, as values of # > #/2 would give negative values for P which are meaningless. However #max=#/2 gives @min=O and Pmax=@@, therefore #max should be less than 2/2. For example, if max=/4, Pmin=1/3 and @max=3 (corresponding to #min=-#/4) and using the value of a' and 6, the constant K in equation (12) can be shown to be 1.605 and hence A=1.135.

Therefore for the rotor described,

P1-1 P2-1 s0=sin-' 1.135 + (13) P,+1 P2+1 and

1.135 P2-1 P1-1 #=sin-1 # # - # # (14) cos # P2+1 P1+1 To cope with the 1000 Hz bandwidth required, a rotor speed of 60,000 rpm would be needed using the single pattern previously described. A double pattern would double the bandwidth and so a lower rotor speed of 30,000 rpm would be sufficient and easier to achieve.

For a double pattern equation (11) becomes #/2-2# #-4# P= = (15) #/2+2# #+4# as the angular separation for light/dark boundaries is now 7r/2 as opposed to 7r in the single pattern. This consequently halves the value of zero and if admix is taken to be n/8, for example, the equations equivalent to (12), (13) and (14) are -4K# a=sin-1 # # (16) # where K is the double pattern constant and

P1-1 P2-1 #=sin-1 # 1.135 # + # # (17) P1+1 P2+1 1.135 P2-1 P1-1 #=sin-1 # # - # # (18) cos # P2+1 P1+1 Obviously, it would be possible to have more than two patterns formed on the rotor but there is an accompanying reduction in sensitivity corresponding to each further pattern added to the rotor surface.

For a system where the pick-offs are mounted at an angle other than 45 to the roll axis 8, equations (1) and (2) become a'=sin-' (cos S sin (p-sin S cos # sin #) (19) ss'=sin-1 (cos S sin #+sin S cos # sin #) (20) where S is the angle between the pick-off and the axis which gives the equivalent equations for (9) and (10) of

K P1-1 P2-1 #=sin-1 # # + # # (21) 2 cos S P1+1 P2+1 and K P1-1 P1-1 #=sin#1 # # - # # (22) 2 sin S cos # P2+1 P1+1 The angle S can be shown to limit the latitude angles, a' and ss, which are obtainable in practice.

The constant K depends on the following variables (i) maximum pitch and/or roll angle allowable in the particular system, (ii) maximum pick-off separation angle S, and (iii) the maximum longitude, #max.

Claims (10)

1. A gyroscope comprising sensing means and a rotor having a surface defining at least part of a sphere including an equator of the sphere and portions to each side of the equator, said surface comprising a pattern of two or more areas having respective ones of two different values of a property to which the sensing means is responsive, and said rotor being able to spin about a spin axis which is perpendicular to the plane containing the equator and being able to tilt with respect to the sensing means about at least one axis perpendicular to the spin axis such that, in use, with the rotor spinning and with a given amount of tilt, the sensing means forms an electrical signal having alternately a mark and a space value indicative of the changes in the value of said property along a line of latitude around the surface, which line of latitude is at a latitude angle relative to the equator dependent upon the amount of tilt and being positive for latitudes to one side of the equator and negative for latitudes to the other side of the equator, the pattern being such that the mark-space ratio P of the electrical signal- is related to the latitude angle a by the equation:

K(P-1) a=sin-' P+1

2. A gyroscope according to claim 1, wherein said sensing means comprises optoelectrical transducing means and the property of the surface to which the sensing means is responsive is an optical property.

3. A gyroscope according to claim 2, wherein said optical property is reflectivity of the surface.

4. A gyroscope according to claim 2, wherein said optical property is colour of the surface.

5. A gyroscope according to any one of the preceding claims, wherein said sensing means comprises first and second sensors, each operable to provide an electrical signal indicative of the changes in value of the property along a line of latitude around the surface, the first and second sensors being positioned so that when the rotor is tilted relative to the sensing means about only one axis perpendicular to said spin axis, the first and second sensors form respective electrical signals indicative of the changes along the same line of latitude at one side of the equator and, when the rotor is tilted only about the other axis perpendicular to the spin axis, the first and second sensors form respective electrical signals indicative of the changes along respective lines of latitude equispaced but at respective opposite sides of the equator.

6. A gyroscopic sensing system for measuring pitch and roll of a missile, the system comprising: a gyroscope rotor having a spherical surface respective parts of which have different values of optical reflectivity, the boundary between said parts being defined by an inverse sine function; first and second optical sensors for sensing the reflectivity of respective adjacent portions of said surface and thereby forming output signals indicative of the position of the rotor; and processing means for processing said output signals to provide said pitch and roll measurements.

7. A system according to claim 6, wherein said inverse sine function relates the angle of longitude J and the angle of latitude a of a point on said boundary according to the equation

-2K# a=sin-1 # # #

8.A gyroscopic sensing system comprising: a rotor which spins about a spin axis and tilts about two further axes, each further axis being perpendicular to said spin axis and to one another, the rotor having a spherical surface on which is formed a pattern of differing reflectivity, the boundary between differing reflectivities being defined by an inverse sine function which relates the angles of latitude and longitude, a and , of each point on the boundary; first and second sensing means mounted at an angle S to one of said perpendicular axes and each being operable to form electrical output signals corresponding to respective mark-space ratios P, and P2 which are indicative of the reflectivity of the pattern along lines of latitude around the spherical surface; and processing means for processing said output signals to provide respective measurements of tilt, 0 and 6, about said two axes.

9. A system according to claim 8, wherein said processing means comprises a microprocessor coupled to a programmable read-only memory (PROM), the microprocessor being operable for evaluating equations to determine said measurements of tilt using look-up values stored in the PROM, the equations being

K P1-1 P2-1 #=sin-1 # # + # # 2 cos S P1+1 P2+1 and K P2-1 P1-1 #=sin-1 # # - # # 2 sin S cos # P2+1 P1+1

10. A gyroscope substantially as hereinbefore described with reference to the accompanying drawings.