Jack Kuipers

Jack Kuipers (Jack B. Kuipers, 1921-2016) was an inventor who worked on 3D tracking at Polhemus. He was a mathematician and aerospace engineer from Grand Rapids, Michigan, and taught mathematics at Calvin College in that city until he retired from its faculty in 1986. His patents from the 1970s describe a way to measure both the position and the orientation of a remote object by generating and sensing low-frequency magnetic fields. In 1979, engineers at Polhemus Navigation Sciences published an analysis of a magnetic position and orientation tracking system for head tracking, describing it as "a position and orientation measurement concept invented by J. Kuipers".

He did work on quaternions. He wrote a book titled Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace, and Virtual Reality. Princeton University Press, which publishes the book, describes him as "regarded by some as the founder of virtual reality".

He is the inventor of Polhemus' patent US 3,983,474.

Reviewed 27 September 2026. Biography, career dates, patent details, the 1979 and 1980 IEEE papers and book details checked against the Calvin finding aid, archived obituary, Google Patents, Crossref and Princeton University Press. About review dates.

Early life and education

Kuipers was born in 1921 in Grand Rapids, Michigan, the oldest of eight children of Berend and Grace (née Werkeman) Kuipers. He majored in mathematics and physics at Calvin College, graduating in 1942. He served with the US Army Signal Corps during World War II; Calvin's 2016 obituary places his service in the European theater. The biographical note in his archival collection lists a BS in electrical engineering and an MS in automatic control engineering from the University of Michigan, along with study of radar technology at MIT and Harvard University. The Calvin obituary states that he earned three degrees from the University of Michigan in addition to his Calvin degree.

Career

Aerospace industry

Kuipers worked for aerospace contractors during the 1950s and taught control and information theory on the staff of the University of Michigan in the 1960s. Calvin's obituary says he spent almost 20 years in industrial engineering, including work on weapons systems for the U.S. Air Force during the Cold War, and that in the 1950s he began working on the mathematics used to produce simulations for Air Force pilots, developing what the college called a "six-dimensional graphics system". Princeton University Press gives the length of his aerospace career as seventeen years and says his work there included applying quaternion theory to aerospace systems.

His papers at Calvin include engineering reports for Lear Incorporated from 1953 to 1958, analysis for a B-70 brake system project from 1959 to 1961, subcontract work with Nortronics in 1969, and consulting reports for Jet Electronics and Technology Incorporated in 1973. An early patent, US 3,474,241 (filed 1966, granted 1969), covers a coordinate transformer for obtaining Euler angle rates of change for a body. A second, US 3,660,648 (granted 1972), converts body-axis angular rate signals into Euler angle rates in a way intended to avoid difficulties equivalent to the gimbal-lock problem of gyroscopes.

Calvin College

Kuipers returned to his alma mater to teach mathematics. Calvin's 2016 obituary dates his arrival to 1966, while the finding aid for his papers gives 1967; both sources agree that he retired in 1986 and became professor emeritus. In the obituary he is quoted as saying he left defense work because "I needed to get away from that". He continued research and consulting while on the faculty and after retiring: the collection records consulting agreements with Calvin College in 2000 and 2001, and his Google Scholar profile lists him as professor emeritus of mathematics at Calvin College. Calvin named him a Distinguished Alumnus in 2002.

Electromagnetic tracking

Kuipers's electromagnetic tracking work centered on a system called SPASYN, short for "space synchronizer". The Calvin archives describe it as using radio signals to determine the relationship between two objects moving through three-dimensional space, and say the technology was adapted to guidance and targeting systems, air traffic control and virtual reality.

His patent US 3,868,565, filed on July 30, 1973 and granted on February 25, 1975, describes a magnetic field that nutates about a pointing vector. Mutually orthogonal coils produce the field, and sensors on the object measure it along at least two orthogonal directions, so the system can locate the object and determine its orientation relative to the generating coils. Two follow-on patents were assigned to Polhemus Navigation Sciences Inc.: US 3,983,474, filed in February 1975 and granted on September 28, 1976, uses orthogonal dipole radiators and orthogonal sensors with coordinate transformation to measure five independent angles (two giving the object's direction and three its orientation), and US 4,017,858, granted on April 12, 1977, covers apparatus for generating the nutating field. Kuipers and A. R. DeRuyck also wrote a November 1973 technical report for the Air Force Avionics Laboratory, "An electromagnetic position sensor", issued by Polhemus Navigation Sciences in Burlington, Vermont.

The 1979 paper by Frederick H. Raab and three colleagues at Polhemus Navigation Sciences, then a subsidiary of The Austin Company, analyzed a system based on Kuipers's concept and cited his three patents. It used a three-axis magnetic-dipole source and a three-axis magnetic sensor, which together gave enough information to determine the sensor's position and orientation in six degrees of freedom. The paper discussed head tracking for helmet-mounted sights, in which the sensor sits on a pilot's helmet and the source is mounted above and behind the head, for example on the aircraft canopy. It gave typical carrier frequencies of 7 to 14 kHz and measurement update rates of 30 to 120 Hz.

Kuipers described the system himself in "SPASYN-an electromagnetic relative position and orientation tracking system", published in IEEE Transactions on Instrumentation and Measurement in December 1980. The paper relates two remote body coordinate frames in position and orientation using antenna triads fixed in each body, and presents near-field and far-field processing strategies. A related paper by Kuipers, "TWOWAY, a position and orientation measurement system", appeared in the proceedings of the OCEANS '77 conference.

Later patents extended the work. US 4,298,874, filed in 1978, granted in 1981 and assigned to The Austin Company, covers two bodies that each carry radiating antennas and exchange electromagnetic fields, so that each can determine its orientation relative to the other; measuring the distance between them by phase-locking gives a full six-degree-of-freedom measurement. US 4,742,356, filed in 1985, granted on May 3, 1988 and assigned to McDonnell Douglas Corporation, processes electromagnetic field measurements into position and orientation. Its text describes mounting a three-axis sensor in a pilot's helmet to find the line of sight, and a real-time binocular computer graphics application that generates a pilot's cockpit view in a flight simulator.

According to the finding aid for his papers, Kuipers held eight patents in the United States and nine in other countries. The collection's patent-litigation series includes files on his cases against The Austin Company (1985) and McDonnell Douglas Corporation (1987 to 2000, including 2000 mediation statements and settlement correspondence), and his 1992 testimony in a case between Polhemus and Ascension Technology.

Quaternions and Rotation Sequences

Quaternions and Rotation Sequences (copyright 1999) introduces quaternions for scientists and engineers and presents them alongside the conventional 3 x 3 rotation matrix so that readers can compare the two approaches. Its final part covers applications, including a six degree-of-freedom electromagnetic position and orientation transducer and the computer graphics needed for virtual reality applications. Princeton University Press lists the paperback at 394 pages with 121 figures, published on September 8, 2002. According to a 2002 profile in Calvin's alumni magazine, quoted in the college's obituary, Kuipers spent 10 years typing the book and drew all 121 diagrams himself. He said of it: "I'm an applied person, not a theoretician. That's what makes this book different." His archived papers include chapter drafts from 1996 and a 1999 lecture on the subject given at the Bulgarian Academy of Sciences.

Peter Rowlands, reviewing the book in Contemporary Physics, called it "everything one could wish for in a primer". The book is the most cited entry on Kuipers's Google Scholar profile.

Personal life and death

Kuipers married Lois Belle Holtrop, and they had five children. He died on April 27, 2016, at the age of 95.

Legacy

Calvin University's Heritage Hall holds the Jack B. Kuipers Collection (COLL/160), 12 boxes of papers dated 1953 to 2006. It contains his SPASYN research, patent files, consulting reports, book drafts and correspondence, and the archive's abstract describes him as a "pioneer in virtual reality technology". Calvin's 2016 obituary wrote that his work in the 1950s "led many to consider Kuipers the father of virtual reality".

See also

• Head tracking
• Helmet-mounted display
• History of virtual reality