Type synthesis of mechanisms aims to systematically determine all possible structures for a specific mobility requirement. Numerous methods based on di erent theories were proposed for type synthesis of lower mobility...Type synthesis of mechanisms aims to systematically determine all possible structures for a specific mobility requirement. Numerous methods based on di erent theories were proposed for type synthesis of lower mobility parallel mechanisms in past decades. However, there does not exist a comprehensive review on these approaches. Therefore, the goal of this paper is to give such a review, classifying the approaches proposed in the literature into three groups, namely, motion-based methods, constraint-based methods, and other methods. The motion-based methods include the Lie group based method, the GF set method, the linear transformation method, the POC set method,and the finite screw method. The constraint-based methods involve the screw theory-based method, the virtual chain method, the method based on Grassmann line geometry and line graphs, and the motion constraint generator method. Other methods contain the enumeration approach based on the general CGK mobility formula and the graph theory method. Upon thoroughly analyzing the characteristics and/or limitations of each method, this review provides a well reference to help researchers find an e ective synthesis method for innovative design and further scientific investigations for mechanisms.展开更多
One of the key issues for parallel mechanism is the kinematic characteristics,especially the workspace which varies with configuration parameters.A kind of 4UPS-UPU parallel mechanism is designed and its workspace is ...One of the key issues for parallel mechanism is the kinematic characteristics,especially the workspace which varies with configuration parameters.A kind of 4UPS-UPU parallel mechanism is designed and its workspace is studied in this paper.First,the mobility of the 4UPS-UPU parallel mechanism is analyzed based on the reciprocal screw theory,and the motion and constraint screw systems of the parallel mechanism are obtained.Then the inverse kinematics is derived by the closed-form kinematics chain.The boundary search method in the polar coordinate system is presented to analyze the constant-orientation workspace of the parallel mechanism.Finally,the influence factors relevant to the workspace,such as the structural parameters and kinematics parameters are analyzed in detail.The relationship between the workspace volume and different parameters are obtained.The conclusions can be used for parameters optimization and path planning of the parallel mechanism.展开更多
Type synthesis of lower-mobility parallel mechanisms is a hot and frontier topic in international academic and industrial field. Based on the Lie group theory, a displacement manifold synthesis method is proposed. For...Type synthesis of lower-mobility parallel mechanisms is a hot and frontier topic in international academic and industrial field. Based on the Lie group theory, a displacement manifold synthesis method is proposed. For all the nine kinds of lower-mobility parallel mechanisms, the mechanism displacement manifold, limb displacement manifold and the geometrical conditions which guarantee that the intersection of the limb displacement manifold is the desired mechanism displacement manifold are enumerated. Various limb kinematic chains can be obtained using the product closure of displacement subgroup. Parallel mechanisms can be constructed with these limbs while obeying the geometrical conditions. Hence, all the nine kinds of lower-mobility parallel mechanisms can be synthesized using this method. Since displacement manifold deals with finite motion, the result mechanism of synthesis have full-cycle mobility. Novel architectures of lower-mobility parallel mechanisms can be obtained using this method.展开更多
Motion type (or motion pattern) of a mechanism is defined as the set of all rigid motions achievable by the mechanism’s end-effector;the motion type of a parallel mechanism equals the intersection set of all subchain...Motion type (or motion pattern) of a mechanism is defined as the set of all rigid motions achievable by the mechanism’s end-effector;the motion type of a parallel mechanism equals the intersection set of all subchain motion types.The motion type of a non-instantaneous parallel mechanism locally agrees with a regular submanifold (or a Lie subgroup in particular) of the special Euclidean group SE(3).Based on submanifold germs of SE(3), we can define an equivalence relation and a partial order relation for both motion types and parallel mechanisms: two motion types are equivalent if and only if they agree on an open neighbor-hood around the identity element of SE(3);two motion types are comparable if and only if one is a submanifold of the other on an open neighborhood around the identity of SE(3).It is also possible to define equivalence relation and partial ordering on the col-lection of parallel mechanisms.In this paper, we first study properties of the equivalence and partial order relation of both motion types and parallel mechanisms, then we discuss their application in type synthesis, mobility analysis and non-overconstrained ness realization of parallel mechanisms.展开更多
It is well known that the traditional Grübler-Kutzbach formula fails to calculate the mobility of some classical mechanisms or many modern parallel robots,and this situation seriously hampers mechani-cal innovati...It is well known that the traditional Grübler-Kutzbach formula fails to calculate the mobility of some classical mechanisms or many modern parallel robots,and this situation seriously hampers mechani-cal innovation.To seek an efficient and universal method for mobility calculation has been a heated topic in the sphere of mechanism.The modified Grübler-Kutzbach criterion proposed by us achieved success in calculating the mobility of a lot of highly complicated mechanisms,especially the mobility of all recent parallel mechanisms listed by Gogu,and the Bennett mechanism known for its particular difficulty.With wide applications of the criterion,a systematic methodology has recently formed.This paper systematically presents the methodology based on the screw theory for the first time and ana-lyzes six representative puzzling mechanisms.In addition,the methodology is convenient for judgment of the instantaneous or full-cycle mobility,and has become an effective and general method of great scientific value and practical significance.In the first half,this paper introduces the basic screw theory,then it presents the effective methodology formed within this decade.The second half of this paper presents how to apply the methodology by analyzing the mobility of several puzzling mechanisms.Finally,this paper contrasts and analyzes some different methods and interprets the essential reason for validity of our methodology.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.51705465,51525504)Young Researchers Foundation of Zhejiang Provincial Top Key Academic Discipline of Mechanical Engineering of Zhejiang Sci-tech University(Grant No.ZSTUME02B02)
文摘Type synthesis of mechanisms aims to systematically determine all possible structures for a specific mobility requirement. Numerous methods based on di erent theories were proposed for type synthesis of lower mobility parallel mechanisms in past decades. However, there does not exist a comprehensive review on these approaches. Therefore, the goal of this paper is to give such a review, classifying the approaches proposed in the literature into three groups, namely, motion-based methods, constraint-based methods, and other methods. The motion-based methods include the Lie group based method, the GF set method, the linear transformation method, the POC set method,and the finite screw method. The constraint-based methods involve the screw theory-based method, the virtual chain method, the method based on Grassmann line geometry and line graphs, and the motion constraint generator method. Other methods contain the enumeration approach based on the general CGK mobility formula and the graph theory method. Upon thoroughly analyzing the characteristics and/or limitations of each method, this review provides a well reference to help researchers find an e ective synthesis method for innovative design and further scientific investigations for mechanisms.
基金Supported by the National High Technology Research and Development Programme of China(No.SS2012AA041604)
文摘One of the key issues for parallel mechanism is the kinematic characteristics,especially the workspace which varies with configuration parameters.A kind of 4UPS-UPU parallel mechanism is designed and its workspace is studied in this paper.First,the mobility of the 4UPS-UPU parallel mechanism is analyzed based on the reciprocal screw theory,and the motion and constraint screw systems of the parallel mechanism are obtained.Then the inverse kinematics is derived by the closed-form kinematics chain.The boundary search method in the polar coordinate system is presented to analyze the constant-orientation workspace of the parallel mechanism.Finally,the influence factors relevant to the workspace,such as the structural parameters and kinematics parameters are analyzed in detail.The relationship between the workspace volume and different parameters are obtained.The conclusions can be used for parameters optimization and path planning of the parallel mechanism.
基金the National Natural Science Foundation of China (Grant No. 50075074).
文摘Type synthesis of lower-mobility parallel mechanisms is a hot and frontier topic in international academic and industrial field. Based on the Lie group theory, a displacement manifold synthesis method is proposed. For all the nine kinds of lower-mobility parallel mechanisms, the mechanism displacement manifold, limb displacement manifold and the geometrical conditions which guarantee that the intersection of the limb displacement manifold is the desired mechanism displacement manifold are enumerated. Various limb kinematic chains can be obtained using the product closure of displacement subgroup. Parallel mechanisms can be constructed with these limbs while obeying the geometrical conditions. Hence, all the nine kinds of lower-mobility parallel mechanisms can be synthesized using this method. Since displacement manifold deals with finite motion, the result mechanism of synthesis have full-cycle mobility. Novel architectures of lower-mobility parallel mechanisms can be obtained using this method.
基金supported by the National Basic Research Program of China (2006CB705400)Science & Technology Commission of Shanghai Municipality (071111008)Research & Development Program of China (2006AA4z334)
文摘Motion type (or motion pattern) of a mechanism is defined as the set of all rigid motions achievable by the mechanism’s end-effector;the motion type of a parallel mechanism equals the intersection set of all subchain motion types.The motion type of a non-instantaneous parallel mechanism locally agrees with a regular submanifold (or a Lie subgroup in particular) of the special Euclidean group SE(3).Based on submanifold germs of SE(3), we can define an equivalence relation and a partial order relation for both motion types and parallel mechanisms: two motion types are equivalent if and only if they agree on an open neighbor-hood around the identity element of SE(3);two motion types are comparable if and only if one is a submanifold of the other on an open neighborhood around the identity of SE(3).It is also possible to define equivalence relation and partial ordering on the col-lection of parallel mechanisms.In this paper, we first study properties of the equivalence and partial order relation of both motion types and parallel mechanisms, then we discuss their application in type synthesis, mobility analysis and non-overconstrained ness realization of parallel mechanisms.
基金Supported by the National Natural Science Foundation of China (Gratn Nos. 50875227, 50575197)
文摘It is well known that the traditional Grübler-Kutzbach formula fails to calculate the mobility of some classical mechanisms or many modern parallel robots,and this situation seriously hampers mechani-cal innovation.To seek an efficient and universal method for mobility calculation has been a heated topic in the sphere of mechanism.The modified Grübler-Kutzbach criterion proposed by us achieved success in calculating the mobility of a lot of highly complicated mechanisms,especially the mobility of all recent parallel mechanisms listed by Gogu,and the Bennett mechanism known for its particular difficulty.With wide applications of the criterion,a systematic methodology has recently formed.This paper systematically presents the methodology based on the screw theory for the first time and ana-lyzes six representative puzzling mechanisms.In addition,the methodology is convenient for judgment of the instantaneous or full-cycle mobility,and has become an effective and general method of great scientific value and practical significance.In the first half,this paper introduces the basic screw theory,then it presents the effective methodology formed within this decade.The second half of this paper presents how to apply the methodology by analyzing the mobility of several puzzling mechanisms.Finally,this paper contrasts and analyzes some different methods and interprets the essential reason for validity of our methodology.
