a fundamental mechanical element of this invention is the spherical surface of outer shell 1 , the motion of which is driven by the wheels of two assemblies . each such assembly comprises a single wheel , or a pair of wheels , frictionally contacting the spherical surface ; associated motors ; and a mounting arrangement . the mounting arrangement provides for the wheel axis direction to be changed , thereby changing the direction of motion of the sphere . outer shell 1 supports the entire moving platform . fig1 is a partial sectional view with some parts rotated into the plane of the view as is commonly done in good drafting practice . it shows outer shell 1 resting on freely - rotating ball 8 in its mount 9 , and one of the drive wheels 10 on its mechanism and mount 11 . fig3 shows the ball and drive wheels arranged in a triangular pattern on the base plate 15 . drive wheel 10 and its mechanism 11 have controlled bidirectional motors and gears that drive the rotation of each wheel about its axis , and set the direction of the wheel axis , hence the direction of wheel action . u . s . pat . no . 5 , 490 , 764 shows three arrangements for mechanisms of this type ( in that patent &# 39 ; s fig4 , 5 , and 6 ). fig4 shows another arrangement for the wheel mechanism . in that figure , wheels 10 are mounted on freely pivoting frame 50 . the axles of the wheels have a common centerline . motors driving the wheels are in fixed frame 51 . mounting plate 72 supports the mechanism . the wheels frictionally contact outer surface 79 of outer shell 1 and drive the shell &# 39 ; s motion . the direction of wheel action is determined by controlled differential rotation of the two wheels 10 , which causes freely pivoting frame 50 to rotate . this mechanism is described in more detail in u . s . patent application ser . no . 62 / 117 , 491 . one unique feature of this invention is retainer plate 7 , which is rigidly mounted on base plate 15 using mount 13 . the retainer plate prevents tipping of outer shell 1 , hence that of the moving platform . mount 13 passes through a clearance opening , shown as edge 18 , in outer shell 1 . while the retainer plate and its mount limit the range of motion of the outer shell , a preferred arrangement will allow sufficient motion for the intended applications . for the configuration shown in fig1 , roll and pitch can range at least from − 15 to + 15 degrees . yaw is unlimited . shroud 17 encloses the movement mechanism . base plate 15 rests on floor surface 16 . in the moving platform , inner shell 4 , which separates the rider space from retainer plate 7 , is attached to outer shell 1 by shell closure 38 . fig1 shows inner shell 4 as a spherical section , but the shape is not important as long as it provides clearance for retainer plate 7 , and structural support for seat 21 and the rider . seat 21 , which is mounted on seat mounting bracket 22 , has a movable bracket 36 to support the computer tablet within view of the rider . fig1 shows the alternate position 37 of bracket 36 when it has been moved to an out - of - the - way position . various rider - operated controls 27 , including , for example , a joystick 26 , are be mounted on the seat . the computer tablet is bidirectionally linked , preferably by wireless connections , to controls that are not part of the computer tablet and to an electronics module ( not shown in the figures ) in the base unit . that electronics module produces the electrical signals powering the motors of the drive - wheel assemblies . it is useful to have some mathematical notations for describing control of the drive wheels . to that end , identify each wheel assembly with a number 1 or 2 , wheel assembly 1 being the first one encountered in moving from the support ball in a counterclockwise direction around the center of base 15 as seen from above , and wheel assembly 2 being the other one . in the following , k will denote either wheel number , and “ sphere ” will mean the sphere of the exterior surface of outer shell 1 . let u k be the unit vector pointing from the center c of the sphere toward wheel assembly k . more specifically , u k points toward a point p k defined as follows : if wheel assembly k has a single wheel , then p k is the point at which the wheel contacts the spherical surface ; if wheel assembly k has a pair of wheels , p k is midway between the points at which the two wheels contact the spherical surface . see fig5 . the two vectors u 1 and u 2 and the center c determine a plane p . let w denote the unit vector orthogonal to p and pointing in the direction of motion of a right - handed screw rotating about c from p 1 to p 2 . in conventional vector notation , w =( u 1 × u 2 )/| u 1 × u 2 |, where × is the usual vector cross product , and the denominator is the length of u 1 × u 2 . let v k = w × u k . then u k , v k , and w are unit basis vectors for a right - handed coordinate system . fig5 shows the plane p and the sphere &# 39 ; s great circle 40 intersection with p . the great circle has its center at c , and it passes through wheel points p 1 and p 2 . the figure also shows a rotation vector r and the circle of rotation 41 associated with r . coordinate vectors u 1 , u 2 , v 1 , v 2 , and w ( the latter in two places ) are shown moved to the corresponding wheel points p 1 and p 2 . let r 1 , and r 2 be the rotation vectors associated with sphere rotation due to the drive wheels at p 1 , and p 2 , respectively . since each of these is orthogonal to the corresponding u k , these can be expressed as follows : where β 1 , γ 1 , β 2 , and γ 2 are numbers . the vectors γ 1 w and γ 2 w represent rotations in the plane p . in order that there be no conflict ( i . e ., jamming ) between drive wheels at p 1 and p 2 , these must be equal , so where γ is the common value of γ 1 and γ 2 . the vector β 1 v 1 represents a rotation orthogonal to the plane p . that rotation must have p 2 as a fixed point because drive - wheel friction will block non - zero motion there ( unless the drive - wheel motion at that point is identical to that caused by the rotation β 1 v 1 ). the only way that this can be guaranteed is for the line through c and p 2 , the axis of this rotation , to be parallel to v 1 . the same argument can be applied to β 2 v 2 , mutatis mutandis , of course . thus , p 1 and p 2 must be positioned so that u 1 and u 2 are orthogonal . this is the same as requiring that the lines from c to each of p 1 and p 2 be orthogonal , which is assumed henceforth . the overall rotation , represented by the vector r , is a combination of r 1 and r 2 . it is the sum of the orthogonal in - plane components and the out - of - plane component : the first step in controlling sphere motion is determining β 1 , β 2 , and γ from a given r . then those values are used to set the direction and speed of the drive wheels . since v 1 , v 2 , and w are mutually orthogonal , this is just a matter of computing vector dot products : drive wheel rotations r w1 and r w2 at p 1 and r 2 , respectively , are where ρ is the ratio of sphere radius to drive wheel radius , and the minus sign arises from the fact that wheel rotation is opposite to the corresponding sphere rotation . the timed sequence of rotations generated by the computer tablet are sent through the wireless link to the electronics module in the base unit . that module receives the required rotations , and converts them to signals controlling the motors of the drive - wheel assemblies . the electronics module also determines the position of the moving unit , for example using an optical or magnetic sensor and corresponding marks on or magnets in the outer shell , and sends the position information back to the computer tablet in the moving unit . methods for doing this will be apparent to persons knowledgeable of the relevant art . fig6 shows a possible organization for control . the dashed line separates the part in the moving platform from that in the base unit . the part in the moving platform centers on the computer tablet , which communicates with other controls , preferably by wireless links . control commands are communicated through the wireless module of the computer tablet to the wireless module in the electronics module of the base unit . the most common command is to rotate the sphere according to rotation vector r to a particular position , as indicated by the angle θ . consecutively arriving values of the pair & lt ; r , θ & gt ; are pushed into the first - in , first - out register ( fifo ). they are passed on at appropriate times . fig6 shows one other type of command , the align command . the pitch and roll positions of the moving platform are estimated using accelerometers in the computer tablet or other controls . yaw position is determined by integrating the rotation rate obtained from drive wheel rotation and direction . each of these positions is subject to drift , integration errors , or changing of the position of the computer tablet , so it is necessary to realign the moving platform occasionally . the electronics module has an alignment timeout unit which issues an align command at appropriate times . the or element combines commands so that an align command is issued to the alignment control unit if the command is received from either the wireless module or the alignment timeout element . when the alignment control unit receives an align command , it issues a reset signal to the alignment timeout unit , thereby starting the time interval to the next timeout ; then it begins issuing rotation pairs & lt ; r , θ & gt ;. the select by priority unit passes the & lt ; r , θ & gt ; pairs to the compute β 1 , β 2 , γ unit , with commands from alignment control having priority over those from fifo . the values of β 1 , β 2 , and γ are passed to the wheel motor control , which generates signals to the motors of the drive - wheel assemblies . the electronics module has a position sensing unit which supplies some information about the sphere position to the alignment unit and , through the wireless connection , to the computer tablet . in a preferred embodiment , the position sensor uses optical or magnetic means to determine sufficient information for homing ( realigning ) the moving platform . for example , an optical means might sense only a few optically contrasting marks on the sphere . one such mark is sufficient to establish a home position for yaw . a single optical sensor can be used for homing as follows : if yaw is moved to the home position first , a mark across the yaw mark is sufficient for homing pitch ; roll can then be homed by using small movements of the sphere to test the orientation of the yaw mark . more complex optical patterns can be used if more complete position information is needed . the possibility of using more marks and / or optical sensors to obtain more complete position information will be apparent to persons familiar with the relevant art . the computer tablet generates commands for whatever motion simulation is being done . a single installation of this invention can be used for such activities as aircraft flight simulation , auto driving simulation , space trip simulation , etc . each kind of simulation has a corresponding app . the exact nature of such apps is not a part of this invention , but persons familiar with the relevant art would be able to develop apps for particular applications . it will be apparent to persons familiar with the relevant art that a freely rotating ball can be replaced by a caster or a drive - wheel assembly . in the latter case , the electronics module must coordinate rotation of all drive wheels .
this motion simulator uses a spherical shape driven by controlled wheels to produce any rotational motion within certain limits . the range of pitch and roll motions can be at least − 15 to + 15 degrees ; yaw is unlimited . there are no moving electrical connections such as slip rings . the physical system can be produced inexpensively . control and simulation display use a smart phone or computer tablet , which , for example , could be one already owned by a family using the simulator .