To address the challenge of calibrating the workspace of Delta parallel robots, this study proposes a general solution framework of searching the maximum inscribed working curve based on density field theory. This method constructs a continuous density field through the statistical modeling of spatial point sets, which transforms the complex boundary determination problem into a density gradient extremum detection problem. It effectively avoids the reliance of traditional geometric methods on the explicit modeling of complex surfaces and simultaneously overcomes the inherent accuracy limitations of numerical discretization methods that depend on the sampling density and require the complex parameter tuning. The core innovation lies in the development of a universal solver that does not rely on additional parameters and a dual-path complementary mechanism: On one hand, the analytical formula method based on kinematic equations achieves high-precision generation of the maximum inscribed curve by precisely calculating the proportion of effective points on the circumference, making it suitable for the structural parameter optimization design; On the other hand, the numerical point set method based on kernel density estimation (KDE) converts discrete point clouds into continuous probability density functions, identifies boundaries using extrema and generates engineering-grade curves with built-in safety margins. Experimental results show that the maximum joint angle deviation of the boundary curve obtained by the analytical formula method does not exceed 0.056°, which strictly satisfies the fourth-axis hyperbolic surface constraint and the spherical hinge rotation angle limit, verifying the accuracy of the solution method. The safety margin experiments demonstrate that compared to the boundary curve derived from the analytical formula method, the boundary curve generated by the numerical point set method proactively reserves a safety margin in the radial direction and can serve as a limit boundary of actual motion control. In conclusion, this method combing the theoretical universality with engineering practicality provides a new theoretical tool for the comprehensive study of trajectory planning, motion control and scaling of high-speed parallel robots.