Lawrence G. Roberts

Lincoln Laboratory, * Massachusetts Institute of Technology
Lexington, Massachusetts.

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An ultrasonic position-sensing device has been designed which will allow a computer to determine periodically the x, y, and z coordinates of the tip of a pensized wand. The device can replace the lightpen and RAND Tablet1 for 2-D work, and extend the usefulness of such devices by virtue of the extra dimension available. The extremely large working space in which the WAND can operate allows it to be used for an entirely new set of pointing functions not directly connected with a display as well as the normal display control functions.

The specifications of the device as it exists on the TX-2 are as follows:

The technique currently being implemented uses four ultrasonic transmitters and one receiver. Each transmitter is pulsed periodically so as to produce a 20-μsec burst of energy, bandpass limited between 20 kc and 100 kc. This burst arrives at the receiver after a time delay proportional to the distance between the two devices. The receiver amplifier is tuned for 50 kc and thus rejects most room noises.

Its output is clipped so that it outputs a pulse when the signal is received. This pulse is used to stop a counter which was started by the pulse to the transmitter. If any reflections are seen by the receiver they occur after the straight path reception and are therefore ignored. Ten milliseconds after one transmitter has been pulsed the next one is pulsed to find the distance between that transmitter and the receiver. In this way the four vector distances to the receiver are determined and thus its position in space can be calculated.

The major inherent advantage of the ultrasonic delay method of determining the position of a stylus is that the measurements are all delay measurements where a digital counter can provide a direct digital readout without requiring an analog to digital conversion. Sound is very convenient for measurement purposes since its propagation velocity is approximately one foot per millisecond. Thus, a 1-megacycle counting rate will resolve distance to .014 inch and a 13-bit counter will allow measurements of up to 9 feet. Allowing time for 11-foot reflections to die out, the transmitters can be pulsed at 10- millisecond intervals. Since four transducers are used, the total cycle takes about 40 milliseconds, providing an operating frequency of 25 cps. The hardware is currently arranged so that the computer is interrupted when a new count is completed, at which time it reads the counter value and the transmitter number (see Fig. 1). It is left to software to calculate the x, y, z coordinates from the four distances.

Figure 1. Block schematic of Lincoln WAND system.


There are two basic kinds of pointing capability which have proven important in graphic activities utilizing a display scope.2, 3 The first, item pointing, provides the machine with the command "that"; the second, position pointing, essentially says "here." Item pointing allows one to select one item out of many displayed on the scope thus facilitating multiple-choice answering or text and drawing editing. The position-pointing capability permits the construction of drawings and the repositioning of symbols on the scope. Without this ability the coordinates of each item would have to be typed in, making drawing extremely inconvenient. Both capabilities can be provided either by an item-pointing device like the light-pen or position-pointing devices like the RAND Tablet and the WAND. An item-pointing device can be extended to provide position information by displaying a tracking cross which follows it; however, the cost in computer time is typically about 5% per console. A position-pointing device can be used to provide item-pointing capability if a hardware or software comparison is made between the coordinates of all points displayed and the position provided by the device. Such a hardware comparator has been built in the TX-2 display generator. The computer merely sends the device position (x, y) to a sample and hold circuit in the scope goes near that position, the analog comparison circuits generate a program interrupt so that the identity of the item being displayed can be recorded. With comparator hardware for the central display generator, position-pointing devices are preferable to light-pens because there is no need to track them; the pointing is more precise, and they will work with long persistence phosphors.


The ability to provide conveniently three-dimensional position information makes it practical to draw lines and curves in three dimensions. Translation of solid objects "stuck" to the WAND is also straightforward. In a slightly less direct manner rotations and viewpoints can be controlled. It is probably not profitable to use the three coordinates from the WAND for more complicated input data (such as rotation angles) unless the transformation is easily comprehended, because the user needs to be able to predict the effect of each movement using the 2-D display mainly for confirmation. An acceptable method of rotating an object would be to "fix" one point on it and move another point. This would control two angles of rotation and the object size. Alternatively, the distance between the fixed and moving point could be ignored to provide pure rotation. Usually, the ability to choose the points eliminates the need for a full three-angle rotation. A viewpoint for a new picture can be specified by first pointing out a new focal point and then specifying the location of the center of the focal plane. This technique provides the translation, perspective, and two rotation angles of a new viewing transformation. The third rotation angle is the extra one which rotates the picture on the scope face and normally would be fixed to keep the horizon horizontal.

In applications where a two-dimensional display is sufficient, the WAND can be used, in effect, as a large-scale RAND Tablet.1 In this case, the z dimension is available as a scalar control. For example, consider the construction of a circuit diagram. There are two basic problems in such a process which usually require the use of a typewriter.

  1. Each component has a numerical value which must be specified in some way to the computer.
  2. Selections from a standard library of parts must be called up onto the screen whenever needed. Also various control buttons are required for specifying functions.

One method of obtaining numbers, parts, or functions which is very distracting is to put down the lightpen or tablet stylus, turn to the keyboard, and type the name or number. An alternative is to point to items around the edge of the display which can be filled with spare parts and control targets. However, there are usually so many parts and functions that several groups of items must be called up and searched to find the desired one. This "tree search" is slow and loads down the edge of the scope with essentially dead pictures and labels.

The WAND provides solutions to both these problems because of its third control coordinate and the large working area. Numbers can be easily modified from their starting values by pointing at them and then "pulling" them up or down with the z axis control. The whole number could be adjusted or the mantissa and exponent separately. If the number were changed exponentially faster with increased velocity, a large dynamic range could be controlled. The large volume available for pointing can be used to point to target areas and pictures of library parts which are completely off the scope. Since the WAND has more range in x and y than the field of the scope and can operate in free space, it can be used to point at large boards of both photographs and typed sheets of function names.

The useful surface area surrounding a scope which would be accessible to the WAND is at least 5000 square inches. Even with one item per square inch this is an impressive library. The advantages of such a setup in reduced display load, preparation time, and specification time are obvious, but perhaps even more significant is the ease with which a user can simply point at what he wants. An even more ambitious step would be to include a 35 mm slide projector with a ground glass screen and have the computer control the slide selection.


The physical layout of the transmitters determines the complexity of calculating the x, y, and z coordinates. However, an even more important consideration is the ease of computing an error check on new measurements before they are accepted.

When a distance is measured the error is usually very small or very large, thus a simple threshold limit on an error measure would eliminate most bad measurements. This is the reason for using four transmitters instead of three. Since any three distances determine the three-space position of the WAND, the fourth provides a geometric check on the measurements. Of course, some sort of dynamic consistency check could be used to reject wild measure- ments; however, when the WAND is jerked, such a check is almost sure to fail. Furthermore, one type of error, the reception of a reflection when the direct path is blocked, is very consistent when it occurs and can only be detected by a geometric check.

In order to provide a simple computation of the error check, the transmitters are placed at the corners of a square or rectangle. This arrangement also allows them to be mounted flush on the front panel of a display scope. Considering a square geometry, assume the origin of the x, y, z coordinate system to be at the center of the square and the transmitters to be at x = a, and z = 0 (see Fig. 2). Since the square of the distance between two points is equal to the sum of the squares of the x, y, and z displacements, assuming the WAND is at (x, y, z), the squares of the four measured distances are as follows:

The computations for x and y are extremely simple.

A relative measure of the error in both x and y is then given simply by

The computation of z is more difficult. Since all the transmitters are in a plane, only z2 can be found. However, it is only necessary to perform one Newton iteration to produce a new z from z2if we use the last value of z as an approximation.


Since the computation of the WAND position must be done continually for each console, unless special hardware is provided, it is important to keep the computation time down. For this reason an incremental technique has been developed.

Given a new distance, d1, for channel 1, the change in d12 between this time and the last time it was sampled (4 units ago) is given by

Figure 2. WAND geometry for receiver and four transmitters.

Then in order to calculate the new value of E we use

or more generally,

Providing we accept this error, we would save the new dn2 and E. Then every fourth time we would compute x, y, and z using Esq. (9a), (9b), (9c), and (5).

These values of x, y, and z are computed from all (not just two) of the distances and thus average out errors better. The computation which is required each 10 milliseconds uses approximately 15 instructions on the TX-2 Computer and about 30 additional instructions every 40 milliseconds. Thus, the time required (on the TX-2) is about 1% of the total computer time.


Occasional errors arise in a gross way in the distance measurements because of room noise (mainly typewriters) triggering the receiver before the pulse is received. This would not occur if the capacitor microphones presently being used as transducers were replaced by more powerful transmitters. At present the error check eliminates a few samples each time a typewriter clanks. Errors also occur when one of the four direct paths is completely blocked. Then the receiver will either miss triggering altogether, which is easily detected, or one of the ever-present reflection paths triggers the receiver. This is the only case when too long a distance is observed. It is difficult to block the path with just a hand or arm unless one intentionally cups a hand over the transmitter. In any case these gross errors are easily rejected by the error check.

There are also fine errors due to the speed of sound changing in the air. A breeze is the most important cause of error of this type and can cause errors from .02-.1 inches in a 3-foot distance. Temperature changes also cause small changes in the speed of sound (about 0.1% per degree). Slow temperature changes mainly affect the absolute accuracy, not the short term stability. In addition to these effects, the pulse width at 50 kc is equivalent to 0.1 inch so the received signal must be detected carefully. Altogether, the fine short-term errors can be as large as about .02 inches in each distance.

Since x and y are computed from the difference of squares of these distances, the error can be magnified. If the transmitters are on a 20" X 20" square and the receiver is three feet away at x = y = 0, then we have unity gain on errors from each distance. That is, a .02" error on one distance would cause .02" error in x and y. However, at six feet away the errors are almost doubled in their effect on x and y.

All effects considered and performance measured, stability of the position is as bad as 0.1" on an instantaneous basis. However, the programs have been designed to include damping of the x, y, and z values. With the damping averaging over 0.1 seconds the stability is about .02" and the tracking of reasonable hand motions is excellent.

The absolute accuracy has not been measured since it is of little importance in man-machine-display work. It is likely to be about 0.2" in the present system but could probably be improved with additional effort.


The Lincoln WAND has been operational since April 1966. In the present configuration, operation has been mainly with test programs to determine the causes of errors and to find remedies in both hardware and software. It is expected that this development will continue. Application programs are also being designed. The WAND operates within the time-sharing system and the expansion to four or five WANDS is being planned. It is possible for all the transmitters in the same room to share the same pulsing logic.

A large portion of the cost of the current WAND is the $1,500 for the ultrasonic equipment which should be reduced considerably in the near future. There are additional costs for the counter, pulser logic and receiver amplifier, but it is apparent that the total cost of the WAND should be competitive with two-dimensional sensors.


  1. M. R. Davis and T. O. Ellis, "The Rand Tablet: A Man-Machine Graphical Communication De- vice," AFIPS FJCC Conference Proceedings, vol. 26, pt. 1, Spartan Books, Baltimore, 1964, pp. 325-31.
  2. Ivan E. Sutherland, "Sketchpad: A Man- Machine Graphical Communication System," AFIPS SJCC Conference Proceedings, vol. 23, Spartan Books, Baltimore, 1963, pp. 329-46.
  3. Timothy E. Johnson, "Sketchpad III-A Computer Program for Drawing in Three Dimensions," AFIPS SJCC Conference Proceedings, ibid, pp. 347-53.
  4. L. G. Roberts, "Machine Perception of Three- Dimensional Solids," MIT Lincoln Laboratory Technical Report No. 315 (May 22, 1963).

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