Geometric Algebra Software for Kinematics

Abstract Geometric algebra (GA), or Clifford algebra, is an alternative to traditional linear algebra for representing/transforming geometric objects. Both formulations date to the mid-19th century, but linear algebra has been a staple in engineering for decades while GA has received scant attention. That balance is shifting as applications are identified where GA offers significant advantages. Physicists started making meaningful use of GA circa 1990, and the computer graphics community started using GA (to replace quaternion rotations) circa 2000. In the last decade, GA started appearing in the engineering literature, especially in works on mechanisms and robot kinematics. The message of this paper is that the time has come for wider adoption of GA in engineering. The key development is the advent of software packages that: (1) are small add-ons to well-known general-use languages; (2) are available free of charge; (3) include integrated graphics; and (4) have manageable learning curves. While GA has broad applicability, we focus on mechanism kinematics and, after an introduction to GA, we show that useful examples can be implemented with small amounts of code.