Functional specification of complex assemblies using projective geometric algebra

In geometric tolerancing, functional specification is becoming challenging as the complex mutual situations of geometrical features increase and the requisites for complex assembly accuracy escalate. A computational representation of sets of situation features is proposed in this paper to manage functional specification of complex assemblies. A minimum triplet set of a point, a straight line and a plane called ToLiP, is introduced to represent situation features. Functional specification operations can thus be mathematically established using projective geometric algebra (PGA). The effectiveness of the proposed approach is highlighted through a case study using quadrupole magnets of a particle accelerator.