少自由度并联机构运动学及五自由度并联机构的相关理论
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摘要
少自由度并联机构近年来成为国际机构学和机器人领域研究的热点。它的运动学研究也随之受到越来越多的关注。在机构运动学分析中,Jacobian矩阵扮演着一个不可或缺的角色。然而对于少自由度并联机构,目前却没有一种统一并实用的建立其Jacobian矩阵的方法。为此,本文基于6自由度并联机构的影响系数法,针对一类少自由度并联机构(机构自由度等于支链自由度数),给出建立其N×N型Jacobian矩阵和N×N×N型Hessian矩阵的方法。同时通过引入仿射坐标系,将该方法发展适用于全部14类少自由度并联机构。利用N×N型Jacobian矩阵找出机构N个输入速度元素与N个独立输出速度元素间的映射关系。并利用坐标变换,为N自由度并联机构(N<6)给出一种建立6×N型Jacobian矩阵的方法。
在现有的少自由度并联机构中,结构对称的5自由度并联机构历史较短,且大部分现有机型的自由度为三转两移。在黄真教授等人于2002年利用基于约束螺旋的型综合理论认清这类机构的约束关系并综合出机构实例后,人们才意识到这类机构的确存在。然而,仅仅意识到事物的存在并不代表认清它的本质。为了加深对该类机构本质的认识并探索这类机型的实用性,本文首先在现存的70余种机型中找出11种机型,并提出7种新机型。这18种机型不仅具有完全对称的结构形式,而且可以采用机架副或与机架相邻的移动副作为驱动副。完全对称的结构形式有助于机构获得近似各向同性的运动学特性。机架副驱动有助于减轻机构的额外负载,提高机构的运行速度。移动副驱动则有助于提高机构的承载能力和加工精度。此外,本文还首次综合出支链结构及安装条件对称的三移两转的并联机构。
运动学是机构分析的重要组成部分。而谈到运动学又不可避免地涉及到机构的奇异位型。由于约束关系的特殊性,5自由度并联机构施加在运动平台上有效约束一般只能为一。因而,这类机型的奇异可以分为两类,即支链内部发生类似于串联机构的奇异以及锁住驱动副后施加在运动平台上的约束螺旋发生线性相关的奇异。本文在前述的18种机型中,找出在奇异分析中具有代表性的6种机型。对它们的这两类奇异都做了详细的阐述和分析。
理论上,完全对称的三转两移5自由度并联机构具有一般性的应用。为了研究这类机型的实用性,本文作者研制了一台5-RRR(RR)并联样机,并实现其控制系统。据本文作者了解,这台样机应是世界上首台该类机构的样机。这台样机的出现不仅为黄真教授等人提出基于约束螺旋的型综合理论的正确性提供了有力的佐证,为研究这类机构的运动特性等提供了依据,而且对该类机型的实用化进行了有益的探索。
Recently, the lower-mobility parallel mechanisms have been one of hot topics in fields of international mechanics and robotics. Hence, kinematics of lower-mobility parallel mechanisms received more and more attention. In the kinematics analysis, Jacobian plays as an important role. However, for a lower-mobility parallel mechanism, there is no unify and practical method to build Jacobian matrix only with structure and configuration parameters. This paper proposed a method to build N×N Jacobian matrix and N×N×N Hessian matrix for a class of lower-mobility parallel mechanism whose mobility of limb equals the mobility of mechanism is also given. Meanwhile, the method is developed to be valid for all 14 classes of lower-mobility parallel mechanisms. A build N×N Jacobian matrix is adopted to show the mapping relationship between N input velocity elements and N independent output velocity elements. Furthermore, the 6×N Jacobian is given by transforming the square Jacobian matrix.
Among the existing lower-mobility parallel mechanisms, the history of 5-DoF parallel mechanism with symmetrical structure is short. Most of them are 3R2T. People realized the existence of this class of mechanisms after some novel mechanism types are synthesized by Prof. Huang and co-workers with the synthesis theory based on constraint screw. However, the essence of one thing cannot be recognized just by inventing. To deepen the cognition on the 5-DoF parallel mechanisms with symmetrical structure, this paper summarized 11 types from more than 70 ones and also proposed 7 ones. The actuators of these 18 mechanisms are symmetrical. Furthermore, they can adopt base-mount-actuator structure or prismatic-actuator-adjacent-to-the-base structure. Symmetrical structure and actuators will be convenient to achieve nearly isotropic kinematics performance. The base-mount-actuator structure could reduce the extra-burden of a mechanism to improve work speed. The prismatic-actuator-adjacent-to- the-base structure will improve the capacity of load and accuracy. Moreover, this paper also synthesized the first 5-DoF 3T2R (three translational and two independent rotational degrees of freedom) with symmetrical structure and assembly condition.
Recently, the lower-mobility parallel mechanisms have been one of hot topics in fields of international mechanics and robotics. Hence, kinematics of lower-mobility parallel mechanisms received more and more attention. In the kinematics analysis, Jacobian plays as an important role. However, for a lower-mobility parallel mechanism, there is no unify and practical method to build Jacobian matrix only with structure and configuration parameters. This paper proposed a method to build N×N Jacobian matrix and N×N×N Hessian matrix for a class of lower-mobility parallel mechanism whose mobility of limb equals the mobility of mechanism is also given. Meanwhile, the method is developed to be valid for all 14 classes of lower-mobility parallel mechanisms. A build N×N Jacobian matrix is adopted to show the mapping relationship between N input velocity elements and N independent output velocity elements. Furthermore, the 6×N Jacobian is given by transforming the square Jacobian matrix.
Among the existing lower-mobility parallel mechanisms, the history of 5-DoF parallel mechanism with symmetrical structure is short. Most of them are 3R2T. People realized the existence of this class of mechanisms after some novel mechanism types are synthesized by Prof. Huang and co-workers with the synthesis theory based on constraint screw. However, the essence of one thing cannot be recognized just by inventing. To deepen the cognition on the 5-DoF parallel mechanisms with symmetrical structure, this paper summarized 11 types from more than 70 ones and also proposed 7 ones. The actuators of these 18 mechanisms are symmetrical. Furthermore, they can adopt base-mount-actuator structure or prismatic-actuator-adjacent-to-the-base structure. Symmetrical structure and actuators will be convenient to achieve nearly isotropic kinematics performance. The base-mount-actuator structure could reduce the extra-burden of a mechanism to improve work speed. The prismatic-actuator-adjacent-to- the-base structure will improve the capacity of load and accuracy. Moreover, this paper also synthesized the first 5-DoF 3T2R (three translational and two independent rotational degrees of freedom) with symmetrical structure and assembly condition.
在现有的少自由度并联机构中,结构对称的5自由度并联机构历史较短,且大部分现有机型的自由度为三转两移。在黄真教授等人于2002年利用基于约束螺旋的型综合理论认清这类机构的约束关系并综合出机构实例后,人们才意识到这类机构的确存在。然而,仅仅意识到事物的存在并不代表认清它的本质。为了加深对该类机构本质的认识并探索这类机型的实用性,本文首先在现存的70余种机型中找出11种机型,并提出7种新机型。这18种机型不仅具有完全对称的结构形式,而且可以采用机架副或与机架相邻的移动副作为驱动副。完全对称的结构形式有助于机构获得近似各向同性的运动学特性。机架副驱动有助于减轻机构的额外负载,提高机构的运行速度。移动副驱动则有助于提高机构的承载能力和加工精度。此外,本文还首次综合出支链结构及安装条件对称的三移两转的并联机构。
运动学是机构分析的重要组成部分。而谈到运动学又不可避免地涉及到机构的奇异位型。由于约束关系的特殊性,5自由度并联机构施加在运动平台上有效约束一般只能为一。因而,这类机型的奇异可以分为两类,即支链内部发生类似于串联机构的奇异以及锁住驱动副后施加在运动平台上的约束螺旋发生线性相关的奇异。本文在前述的18种机型中,找出在奇异分析中具有代表性的6种机型。对它们的这两类奇异都做了详细的阐述和分析。
理论上,完全对称的三转两移5自由度并联机构具有一般性的应用。为了研究这类机型的实用性,本文作者研制了一台5-RRR(RR)并联样机,并实现其控制系统。据本文作者了解,这台样机应是世界上首台该类机构的样机。这台样机的出现不仅为黄真教授等人提出基于约束螺旋的型综合理论的正确性提供了有力的佐证,为研究这类机构的运动特性等提供了依据,而且对该类机型的实用化进行了有益的探索。
Recently, the lower-mobility parallel mechanisms have been one of hot topics in fields of international mechanics and robotics. Hence, kinematics of lower-mobility parallel mechanisms received more and more attention. In the kinematics analysis, Jacobian plays as an important role. However, for a lower-mobility parallel mechanism, there is no unify and practical method to build Jacobian matrix only with structure and configuration parameters. This paper proposed a method to build N×N Jacobian matrix and N×N×N Hessian matrix for a class of lower-mobility parallel mechanism whose mobility of limb equals the mobility of mechanism is also given. Meanwhile, the method is developed to be valid for all 14 classes of lower-mobility parallel mechanisms. A build N×N Jacobian matrix is adopted to show the mapping relationship between N input velocity elements and N independent output velocity elements. Furthermore, the 6×N Jacobian is given by transforming the square Jacobian matrix.
Among the existing lower-mobility parallel mechanisms, the history of 5-DoF parallel mechanism with symmetrical structure is short. Most of them are 3R2T. People realized the existence of this class of mechanisms after some novel mechanism types are synthesized by Prof. Huang and co-workers with the synthesis theory based on constraint screw. However, the essence of one thing cannot be recognized just by inventing. To deepen the cognition on the 5-DoF parallel mechanisms with symmetrical structure, this paper summarized 11 types from more than 70 ones and also proposed 7 ones. The actuators of these 18 mechanisms are symmetrical. Furthermore, they can adopt base-mount-actuator structure or prismatic-actuator-adjacent-to-the-base structure. Symmetrical structure and actuators will be convenient to achieve nearly isotropic kinematics performance. The base-mount-actuator structure could reduce the extra-burden of a mechanism to improve work speed. The prismatic-actuator-adjacent-to- the-base structure will improve the capacity of load and accuracy. Moreover, this paper also synthesized the first 5-DoF 3T2R (three translational and two independent rotational degrees of freedom) with symmetrical structure and assembly condition.
Recently, the lower-mobility parallel mechanisms have been one of hot topics in fields of international mechanics and robotics. Hence, kinematics of lower-mobility parallel mechanisms received more and more attention. In the kinematics analysis, Jacobian plays as an important role. However, for a lower-mobility parallel mechanism, there is no unify and practical method to build Jacobian matrix only with structure and configuration parameters. This paper proposed a method to build N×N Jacobian matrix and N×N×N Hessian matrix for a class of lower-mobility parallel mechanism whose mobility of limb equals the mobility of mechanism is also given. Meanwhile, the method is developed to be valid for all 14 classes of lower-mobility parallel mechanisms. A build N×N Jacobian matrix is adopted to show the mapping relationship between N input velocity elements and N independent output velocity elements. Furthermore, the 6×N Jacobian is given by transforming the square Jacobian matrix.
Among the existing lower-mobility parallel mechanisms, the history of 5-DoF parallel mechanism with symmetrical structure is short. Most of them are 3R2T. People realized the existence of this class of mechanisms after some novel mechanism types are synthesized by Prof. Huang and co-workers with the synthesis theory based on constraint screw. However, the essence of one thing cannot be recognized just by inventing. To deepen the cognition on the 5-DoF parallel mechanisms with symmetrical structure, this paper summarized 11 types from more than 70 ones and also proposed 7 ones. The actuators of these 18 mechanisms are symmetrical. Furthermore, they can adopt base-mount-actuator structure or prismatic-actuator-adjacent-to-the-base structure. Symmetrical structure and actuators will be convenient to achieve nearly isotropic kinematics performance. The base-mount-actuator structure could reduce the extra-burden of a mechanism to improve work speed. The prismatic-actuator-adjacent-to- the-base structure will improve the capacity of load and accuracy. Moreover, this paper also synthesized the first 5-DoF 3T2R (three translational and two independent rotational degrees of freedom) with symmetrical structure and assembly condition.
引文
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