{'fraction_non_alphanumeric': 0.020195439739413682, 'fraction_numerical': 0.001954397394136808, 'mean_word_length': 5.481012658227848, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The Dexterity Analysis of a Spatial Three-Degree of Freedom Parallel Manipulator with Constrained Branch

Abstract—This paper presents a spatial three-degree of freedom (DOF) 3-PUS-UP parallel manipulator with constrained branch that can be employed to high-speed milling for large heterogeneous complex structural component in aerospace field. Taking full consideration of the influence of the actuated branches, the serial constrained branch and the parasitic motion of the terminal moving platform, the closed-loop vector method is employed to deduce the kinematic position inverse solution, the actuation Jacobian matrix and the constrained Jacobian matrix are obtained by resorting to the screw theory and the D-H method, and the uniform full rank Jacobian matrix is constructed. With the help of the matrix condition number and matrix norm theory, the dexterity index characterizing the comprehensive transmission performance of the parallel manipulator is formulated. The distribution pattern of the performance index of the 3-PUS-UP parallel manipulator in the workspace is depicted by some cases, and the performance distribution of the mechanism is briefly investigated, and the optimum workspace region of the dexterity is then drawn in detail. The research results illustrate that the 3-PUS-UP parallel manipulator has good kinematic dexterity, which can be applied to the precision assembly, hybrid machine tool milling, and automobile spraying. Simultaneously, thus it also has a good prospect in engineering application.