Lincoln Wand

Lincoln Wand
Basic Info
Type	Input Devices
Subtype	Ultrasonic tracking
Creator	Lawrence G. Roberts
Developer	MIT Lincoln Laboratory
Release Date	April 1966 (operational on the TX-2)
Requires	TX-2 computer at MIT Lincoln Laboratory
Tracking
Tracking	Pulsed ultrasonic time-of-flight; x, y and z position of the wand tip
Device
Sensors	Four ultrasonic transmitters and one receiver (the wand); capacitor microphones used as transducers
Input	Pen-sized hand-held wand

The Lincoln Wand (written Lincoln WAND in its original paper) was an ultrasonic three-dimensional position-sensing input device developed by Lawrence G. Roberts at the Lincoln Laboratory of the Massachusetts Institute of Technology (MIT) for the laboratory's TX-2 computer. It let the computer read the x, y and z coordinates of the tip of a pen-sized wand about 25 times a second, by timing ultrasonic pulses sent from four transmitters to a receiver in the wand. Roberts reported that the device had been operational since April 1966, and his paper describing it was published in the proceedings of the AFIPS Fall Joint Computer Conference, held in San Francisco on 7-10 November 1966.

The wand was designed as a position-pointing device that could replace the light pen and the RAND Tablet for two-dimensional work and add a third dimension. The paper for a 2005 CHI panel on interaction research at Lincoln Laboratory, organized by Bill Buxton, calls Roberts "the inventor of perhaps the first interactive device for 3D input, the Lincoln Wand". Ivan Sutherland contrasted its pulsed ultrasonic tracking design with the continuous-wave ultrasonic head-position sensor of his 1968 head-mounted three-dimensional display.

Reviewed 21 October 2026. Specifications, design, errors, uses, cost and dates checked against the full 1966 Roberts AFIPS paper; Sutherland 1968, Buxton, Rolland survey, Sketchpad thesis and CHM claims checked against those sources. About review dates.

Development

Roberts built the wand at MIT Lincoln Laboratory in Lexington, Massachusetts, where his paper notes that the work was "operated with support from the Advanced Research Projects Agency". The device was attached to the TX-2, the laboratory computer on which Sutherland had developed Sketchpad. By the mid-1960s the TX-2 ran under a time-sharing operating system and had a point-plotting display, a light pen and the ability to connect arbitrary input and output devices. Roberts's paper states that the wand "operates within the time-sharing system".

The paper reports that the Lincoln Wand had been operational since April 1966. At the time of writing, it had mainly been run with test programs to find the causes of errors and remedies for them in hardware and software, while application programs were still being designed. Sutherland's 1968 paper cites an earlier version of the work as an MIT Lincoln Laboratory report titled "The Lincoln wand", dated June 1966.

Roberts was also a computer graphics researcher. Buxton's panel paper credits him with introducing homogeneous coordinates to represent 3D transformations, an early hidden-line removal algorithm and early work on reconstructing 3D geometry from photographs; around 1966 he and Tom Marill of System Development Corporation also linked the TX-2 with SDC's Q-32/PDP-1 in an early packet-switching network experiment. The Computer History Museum states that ARPA hired Roberts in 1966 as program manager and technical architect for the ARPANET, and that he died on 26 December 2018.

Design and operation

The system used four ultrasonic transmitters and one receiver, the wand. Each transmitter was pulsed in turn to produce a 20-microsecond burst of energy band-limited between 20 kc and 100 kc. The burst reached the receiver after a delay proportional to the distance between the two, and the receiver amplifier, tuned to 50 kc, rejected most room noise. The clipped receiver output stopped a digital counter that had been started by the transmitter pulse. Reflections arrived after the direct-path pulse and were ignored.

Ten milliseconds after one transmitter fired, the next was pulsed, so one cycle through all four took about 40 milliseconds, a rate of 25 cps. The hardware interrupted the computer when each count was complete, and the computer read the counter value and the transmitter number. Software then calculated the x, y and z coordinates from the four distances. Roberts noted that every measurement was a delay measurement, so a counter gave a direct digital readout with no analog-to-digital conversion. Because sound travels at about one foot per millisecond, a 1-megacycle counting rate resolved distance to 0.014 inch, and a 13-bit counter allowed distances of up to 9 feet.

Geometry and computation

The transmitters were placed at the corners of a square or rectangle, which allowed them to be mounted flush on the front panel of a display scope. Three distances are enough to fix a point in space; the fourth gave a geometric check on each new measurement before it was accepted. Roberts chose a geometric check over a dynamic consistency check because a dynamic check was almost sure to fail when the wand was jerked, and because one kind of error, a reflection received when the direct path was blocked, was consistent and could only be detected geometrically.

With a square layout, x and y follow from simple differences of the squared distances, while z is found from z squared with one Newton iteration that uses the previous z as its starting value. To keep the cost low, Roberts used an incremental method. It needed about 15 TX-2 instructions every 10 milliseconds and about 30 more every 40 milliseconds, or about 1% of the computer's time.

Specifications

The paper lists the following specifications for the device as it existed on the TX-2.

Specification	Value (as stated in the 1966 paper)
Working space	4 x 4 x 6 feet
Resolution	.02 inch (12 bits/axis)
Sampling rate	25 cps
Computer time	1%
Absolute accuracy	0.2 inches
Transmitters / receivers	Four transmitters, one receiver (the wand)
Pulse	20-microsecond burst, band-limited between 20 kc and 100 kc
Receiver amplifier	Tuned for 50 kc
Counter	13-bit, 1-megacycle counting rate

Accuracy and error sources

Gross errors came from two sources. Room noise, mainly from typewriters, could trigger the receiver before the pulse arrived; Roberts wrote that this would not happen if the capacitor microphones then used as transducers were replaced with more powerful transmitters, and that the error check removed a few samples each time a typewriter clanked. When one of the four direct paths was completely blocked, the receiver either missed the pulse, which was easy to detect, or triggered on a reflection. Roberts found it hard to block a path with a hand or arm unless a hand was deliberately cupped over a transmitter, and the error check rejected these gross errors.

Finer errors came from changes in the speed of sound. A breeze was the main cause and could produce errors of .02 to .1 inch over a 3-foot distance, and temperature changed the speed of sound by about 0.1% per degree. The pulse width at 50 kc was equivalent to 0.1 inch, so the received signal had to be detected carefully. Short-term errors could reach about .02 inch in each distance. With the transmitters on a 20 x 20 inch square and the wand three feet away, an error in one distance produced an equal error in x and y; at six feet the effect was almost doubled.

Instantaneous position stability was as poor as 0.1 inch, so the programs damped the x, y and z values. With damping that averaged over 0.1 seconds, stability was about .02 inch, and Roberts described the tracking of reasonable hand motions as "excellent". Absolute accuracy had not been measured, since Roberts considered it of little importance in display work; he estimated it at about 0.2 inch.

Proposed uses

Roberts distinguished two kinds of pointing at a display: item pointing, which selects one item out of many displayed, and position pointing, which indicates a location for drawing or repositioning symbols. He classed the light pen as an item-pointing device and the RAND Tablet and the wand as position-pointing devices, noting that either kind could be extended to provide both capabilities. A position-pointing device could select items if its coordinates were compared with those of displayed points. A hardware comparator for this purpose had been built into the TX-2 display generator: the computer sent the wand position to a sample-and-hold circuit in the scope, and an interrupt was raised when a displayed vector or point passed near it. With such hardware, Roberts argued, position-pointing devices were preferable to light pens because they did not need to be tracked, pointed more precisely and worked with long-persistence phosphors.

The third coordinate made it practical to draw lines and curves in three dimensions and to translate objects "stuck" to the wand. Roberts suggested rotating an object by fixing one point on it and moving another, and specifying a new viewpoint by pointing to a new focal point and then to the center of the focal plane. He cautioned that the three coordinates should only drive transformations the user could easily predict, with the 2D display used mainly for confirmation.

For two-dimensional work, Roberts described the wand as a large-scale RAND Tablet whose z axis could act as a scalar control, for example to "pull" a component value up or down in a circuit diagram. Because the wand worked in free space over a larger area than the scope face, it could also point at boards of photographs or typed function names placed around the display; he estimated the usable surface area around a scope at no less than 5000 square inches. He also proposed a computer-controlled 35mm slide projector with a ground glass screen as a further pointing target.

Cost and plans

Roberts wrote that a large part of the wand's cost was $1,500 for the ultrasonic equipment, a figure he expected to fall considerably, with additional costs for the counter, pulser logic and receiver amplifier. He judged that the total cost should be competitive with two-dimensional sensors. An expansion to four or five wands under the time-sharing system was being planned, and Roberts noted that all the transmitters in one room could share the same pulsing logic.

Relation to later ultrasonic tracking

Sutherland's head-mounted display project, which began at Lincoln Laboratory and continued at Harvard University, used an ultrasonic head-position sensor as one of its two trackers. In his 1968 paper Sutherland wrote that, unlike the pulsed Lincoln Wand, his sensor was a continuous-wave system. He chose continuous-wave ultrasound because inexpensive narrow-band transducers were available and to avoid confusion from pulsed noise, such as typewriter noise, "which had caused difficulty for the Lincoln Wand". The trade-off was a wavelength ambiguity of about 1/3 inch in each of the sensor's twelve measurements.

In a survey of tracking technology for virtual environments, Jannick Rolland, Yohan Baillot and Alexei Goon list the "Lincoln laboratory Wand (Roberts, 1966)" as an example of time-of-flight ultrasonic tracking, alongside the Mattel Power Glove, the Logitech RedBaron, the Science Accessories Space Pen and InterSense systems. Buxton's timeline of input devices describes the 1966 "Three-Dimensional Wand" as the first input device he knew of that used ultrasonic sensing, and states that the technology was later used in digitizing tablets, head-tracking assistive devices and 3D video game controllers such as the Power Glove. The timeline's summary gives a resolution of .2 inch in a 4 x 4 x 4 foot volume, which differs from the original paper's figures of .02 inch resolution, about 0.2 inch absolute accuracy and a 4 x 4 x 6 foot working space.

See also

• Ultrasonic tracking system
• Ivan Sutherland's head-mounted 3D display
• Sketchpad
• Positional tracking
• History of virtual reality