• Introduces a novel CGA-based method for forward kinematics of parallel mechanisms with 3-RE structure, eliminating complex algebraic elimination.
• Transforms angular constraints into distance constraints, simplifying geometric modeling and solution.
• Achieves a high-order univariate polynomial equation via tangent half-angle substitution, enabling efficient and coordinate-invariant solutions.
• Validates the approach with a numerical case, demonstrating its effectiveness for complex limb structures.