To investigate the forward kinematics problem of parallel mechanisms with complex limbs and to expand the applicability of the powerful tool of Conformal Geometric Algebra(CGA),a CGA-based modeling and solution method...To investigate the forward kinematics problem of parallel mechanisms with complex limbs and to expand the applicability of the powerful tool of Conformal Geometric Algebra(CGA),a CGA-based modeling and solution method for a class of parallel platforms with 3-RE structure after locking the actuated joints is proposed in this paper.Given that the angle between specific joint axes of limbs remains constant,a set of geometric constraints for the forward kinematics of parallel mechanisms(PM)are determined.After translating unit direction vectors of these joint axes to the common starting point,the geometric constraints of the angle between the vectors are transformed into the distances between the endpoints of the vectors,making them easier to handle.Under the framework of CGA,the positions of key points that determine the position and orientation of the moving platform can be intuitively determined by the intersection,division,and duality of basic geometric entities.By employing the tangent half-angle substitution,the forward kinematic analysis of the parallel mechanisms leads to a high-order univariate polynomial equation without the need for any complex algebraic elimination operations.After solving this equation and back substitution,the position and pose of the MP can be obtained indirectly.A numerical case is utilized to confirm the effectiveness of the proposed method.展开更多
By using the intermediate coordinate-momentum representation in quantum optics and generating function for the normalization of the excited squeezed vacuum state （ESVS）, the normalized ESVS is obtained. We find that...By using the intermediate coordinate-momentum representation in quantum optics and generating function for the normalization of the excited squeezed vacuum state （ESVS）, the normalized ESVS is obtained. We find that its normalization constants obtained via two new methods are uniform and a new form which is different from the result obtained by Zhang and Fan [Phys. Lett. A 165 （1992） 14]. By virtue of the normalization constant of the ESVS and the intermediate coordinate-momentum representation, the tomogram of the normalized ESVS and some useful formulae are derived.展开更多
基金Supported by National Natural Science Foundation of China (Grant No. 52175019)Beijing Municipal Natural Science Foundation of China (Grant No. L222038)+3 种基金Beijing Nova Programme Interdisciplinary Cooperation Project of China (Grant No. 20240484699)Joint Funds of Industry-University-Research of Shanghai Academy of Spaceflight Technology of China (Grant No. SAST2022-017)Beijing Municipal Key Laboratory of Space-ground Interconnection and Convergence of ChinaKey Laboratory of IoT Monitoring and Early Warning,Ministry of Emergency Management of China
文摘To investigate the forward kinematics problem of parallel mechanisms with complex limbs and to expand the applicability of the powerful tool of Conformal Geometric Algebra(CGA),a CGA-based modeling and solution method for a class of parallel platforms with 3-RE structure after locking the actuated joints is proposed in this paper.Given that the angle between specific joint axes of limbs remains constant,a set of geometric constraints for the forward kinematics of parallel mechanisms(PM)are determined.After translating unit direction vectors of these joint axes to the common starting point,the geometric constraints of the angle between the vectors are transformed into the distances between the endpoints of the vectors,making them easier to handle.Under the framework of CGA,the positions of key points that determine the position and orientation of the moving platform can be intuitively determined by the intersection,division,and duality of basic geometric entities.By employing the tangent half-angle substitution,the forward kinematic analysis of the parallel mechanisms leads to a high-order univariate polynomial equation without the need for any complex algebraic elimination operations.After solving this equation and back substitution,the position and pose of the MP can be obtained indirectly.A numerical case is utilized to confirm the effectiveness of the proposed method.
基金The project supported by National Natural Science Foundation of China under Grant No. 10574060 and the Natural Science Foundation of Shandong Provirice of China under Grant No. Y2004A09
文摘By using the intermediate coordinate-momentum representation in quantum optics and generating function for the normalization of the excited squeezed vacuum state （ESVS）, the normalized ESVS is obtained. We find that its normalization constants obtained via two new methods are uniform and a new form which is different from the result obtained by Zhang and Fan [Phys. Lett. A 165 （1992） 14]. By virtue of the normalization constant of the ESVS and the intermediate coordinate-momentum representation, the tomogram of the normalized ESVS and some useful formulae are derived.
