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Singularity analysis of a parallel manipulator (PM) is important in its trajectory planning and workspace design. This paper presents a new method based on geometric algebra (GA) for the singularity analysis of the 3/6‐SPS Gough‐Stewart PM, where S denotes a spherical joint and P a prismatic pair. The 6 line vectors associated with the SPS limb are expressed using GA. An analytic singular polynomial is then derived as the coefficient of the outer product of all 6 line vectors. This polynomial provides an overall description of the singularity of the 3/6‐SPS Gough‐Stewart PM. Position‐singularity loci and orientation‐singularity loci can be drawn based on this polynomial, the latter of which have seldom been addressed. It is also shown that the proposed GA‐based method is geometrically intuitive and computationally efficient.

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