Condition number analysis of a Three Degrees of Freedom Translational Parallel Cube Manipulator

Robot manipulators are geometrically classified into parallel, serial, and hybrid configurations, with parallel manipulators demonstrating superior characteristics including enhanced payload-to-weight ratios, increased structural stiffness, and improved operational accuracy compared to their serial counterparts. This research investigates a three-degree-of-freedom translational parallel cube manipulator through comprehensive kinematic analysis. The study successfully resolves the inverse kinematics problem and derives the corresponding Jacobian matrix, establishing the mathematical foundation for performance evaluation. The condition number serves as a fundamental performance index for quantifying manipulator dexterity and assessing system sensitivity to geometric parameter variations, including link dimensions and moving platform radius, calculated as the ratio between the highest and lowest singular values of the Jacobian matrix. Condition number values are systematically computed across the entire workspace for various geometric parameter ratios, introducing the concept of "well-conditioned" workspace regions where the condition number remains within acceptable bounds. The percentage of well-conditioned workspace area is calculated to evaluate overall manipulator performance. A specialized Python implementation facilitates comprehensive manipulator analysis and computational processing. Results are presented through graphical visualization, demonstrating the relationship between design parameters and workspace performance characteristics, providing valuable insights for optimal manipulator design and operational planning