CN108959812A - A method of based on constraint normal decision mechanism passive constraint - Google Patents
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Abstract
Description
技术领域technical field
本发明属于机械设计领域，具体涉及一种基于约束法线来判断机构虚约束的方法，广泛适合于机器人、并联机床等复杂机构中虚约束的判断。The invention belongs to the field of mechanical design, and specifically relates to a method for judging the virtual constraints of mechanisms based on constraint normals, which is widely suitable for judging virtual constraints in complex mechanisms such as robots and parallel machine tools.
背景技术Background technique
在计算机构自由度的过程中，最重要也是最难以判断的就是机构中的虚约束。机构中是否存在虚约束，哪些构件存在虚约束，这是在分析机构过程中亟待解决的问题，同时这也是限制我们在分析机构的瓶颈，但是目前却没有任何一种适合于所有从业人员判断机构虚约束的通用方法，这就大大限制了我们对于机构更深入的研究。In the process of calculating the degree of freedom of the mechanism, the most important and difficult to judge is the virtual constraint in the mechanism. Whether there are virtual constraints in the organization and which components have virtual constraints are urgent problems to be solved in the process of analyzing the organization. At the same time, this is also the bottleneck that limits our analysis of the organization. However, there is currently no one that is suitable for all practitioners to judge the organization. The general method of imaginary constraints greatly limits our in-depth research on the mechanism.
虽然在探索机构自由度的过程中出现了许多新方法，比如基于运动学分析的方法，基于Jacobian矩阵的方法，基于群论，螺旋代数法，微分几何的方法，基于螺旋理论的方法，以及使用较为广泛的“给定特定几何条件”的经验法等方法，这些方法可以得到机构中的虚约束，但是这些方法都未能得到广泛的应用，其原因可归结为：1）各种方法都没有针对机构中虚约束的具体构件来探索虚约束产生的条件与规律，不便于建立普适性的方法；2）要求使用这有较高的理论水平且分析过程复杂，所以，需要开发一种更加简单，直观，通用的判断机构虚约束的方法。Although many new methods have appeared in the process of exploring the degree of freedom of mechanisms, such as methods based on kinematics analysis, methods based on Jacobian matrix, methods based on group theory, spiral algebra, differential geometry, methods based on spiral theory, and using The more extensive "given specific geometric conditions" empirical method and other methods, these methods can get the virtual constraints in the mechanism, but these methods have not been widely used, the reasons can be attributed to: 1) various methods have no It is not convenient to establish a universal method to explore the conditions and laws of virtual constraints for the specific components of virtual constraints in the mechanism; 2) it requires a high theoretical level and the analysis process is complicated, so it is necessary to develop a more A simple, intuitive and general method for judging the virtual constraints of institutions.
发明内容Contents of the invention
为克服现有技术的不足，本发明提供一种基于约束法线判断机构虚约束的方法，根据机构中约束法线的数量和几何关系判断机构中是否存在虚约束，采用该方法，在分析机构虚约束的过程中更加简单，直观，通用，不需要高深的理论基础和复杂的数学计算，使相关工作人员更易于接受，使用，也更加易于推广。In order to overcome the deficiencies in the prior art, the present invention provides a method for judging the virtual constraints of a mechanism based on the constraint normals, judging whether there are virtual constraints in the mechanism according to the quantity and geometric relationship of the constraint normals in the mechanism, using this method, in analyzing the mechanism The process of virtual constraints is simpler, intuitive, and universal, and does not require advanced theoretical foundations and complex mathematical calculations, making it easier for relevant staff to accept, use, and promote.
本发明的目的是通过以下技术方案实现的：The purpose of the present invention is achieved through the following technical solutions:
一种基于约束法线判断机构虚约束的方法，具体包括以下步骤：A method for judging a virtual constraint of a mechanism based on a constraint normal, specifically comprising the following steps:
（1）将机构中各个运动副均等效成若干个约束点，将约束点处的法线定义为约束法线，所述约束法线分为静法线、动法线、冗余法线，并将各个运动副的静法线、动法线标示出来，所述静法线为两构件之间瞬时相对速度为零的法线，所述动法线为与静法线垂直的法线，所述冗余法线为重复约束某自由度的静法线；(1) Each kinematic pair in the mechanism is equivalent to several constraint points, and the normal at the constraint point is defined as the constraint normal. The constraint normal is divided into static normal, dynamic normal, and redundant normal. And mark the static normal and dynamic normal of each kinematic pair, the static normal is the normal of the instantaneous relative velocity between the two members, and the dynamic normal is the normal perpendicular to the static normal, The redundant normal is a static normal repeatedly constrained to a certain degree of freedom;
（2）将机构中的构件分为同根构件和母体构件，所述母体构件是可与机构中的几个构件形成运动副的构件，所述几个构件即为一组同根构件；(2) Divide the components in the mechanism into the same root component and the parent component, the parent component is a component that can form a kinematic pair with several components in the mechanism, and the several components are a group of common root components;
（3）根据构件各约束点静法线的数量及其几何关系建立判断构件过约束的几何方法，以判断构件是否受到过约束，如果构件不过约束则该构件不存在虚约束，如果该构件存在过约束的情况，则根据该构件各约束点的动法线的速度是否时刻匹配，进而判断构件受到约束的类别，所述约束的类别分为实约束、瞬时虚约束和虚约束。(3) According to the number of static normals of each constraint point of the component and its geometric relationship, a geometric method for judging the over-constraint of the component is established to determine whether the component is over-constrained. If the component is not over-constrained, the component does not have virtual constraints. If the component exists In the case of over-constraint, according to whether the velocity of the dynamic normal of each constraint point of the component matches at all times, and then judge the category of the component constrained, the category of constraints is divided into real constraints, instantaneous virtual constraints and virtual constraints.
进一步的，步骤（3）中根据构件各约束点静法线的数量及其几何关系建立判断构件过约束的方法为：Further, in step (3), the method for establishing over-constraint of a component is established according to the number of static normals of each constraint point of the component and its geometric relationship:
a：非同根构件判断过约束的方法：机构中的一组同根构件同时约束甲构件，且甲构件各约束点处同交于一点的有效法线数量或相互平行的有效法线数量nh大于法线所在空间的维度d时，则甲构件过约束且冗余法线的数量为nh-d；同理，机构中有h组同根构件同时约束甲构件，且各组构件对甲构件同交于一点的有效法线数量或各组相互平行的有效法线数量nh大于d+h-1时，则甲构件过约束且冗余法线的数量为nh-h-d+1；a: The method for judging over-constraint by non-same-rooted components: A group of components with the same root in the mechanism constrains member A at the same time, and the number of effective normals co-intersecting at one point at each constraint point of member A or the number n h of effective normals parallel to each other is greater than When the dimension of the space where the normal line is located is d, the A component is over-constrained and the number of redundant normals is n h -d; similarly, there are h groups of components with the same root constraining the A component at the same time in the mechanism, and each group of components has the same effect on the A component. When the number of effective normals intersecting at one point or the number n h of effective normals parallel to each other is greater than d+h-1, the A member is over-constrained and the number of redundant normals is n h -h-d+1;
b：同根构件判断过约束的方法：机构中有一组同根构件两两相互约束或一组同根构件两两直接约束其它多个构件时，若某同根构件有效法线数量nh在空间内大于6、平面内大于3时，则该构件过约束，且该构件的冗余法线数量在空间内为nh-6，在平面内为nh-3，机构中冗余法线的总数量为各构件冗余法线数量之和。b: The method for judging over-constraint of the same-root component: when there is a group of same-root components pairwise constraining each other in the mechanism or a group of same-root components directly constraining other multiple components, if the effective normal number n h of a certain same-root component is greater than 6 in the space , when the in-plane is greater than 3, the component is over-constrained, and the number of redundant normals of the component is n h -6 in space, n h -3 in the plane, and the total number of redundant normals in the mechanism is The sum of the number of redundant normals of each component.
进一步的，所述有效法线的定义为：乙构件对甲构件的静法线及甲构件对丙构件的静法线统称为甲构件的有效法线。Further, the effective normal is defined as follows: the static normal of component B to component A and the static normal of component A to component C are collectively referred to as the effective normal of component A.
进一步的，步骤（3）中判断过约束构件各约束点的动法线的速度匹配的方法为：A：当过约束构件各约束点处的静法线交于一点时，若各约束点能够保证角速度相等则速度匹配；B：若过约束构件各约束点处的静法线相互平行时，若各约束点线速度方向相同大小相等则速度匹配。Further, in step (3), the method for judging the velocity matching of the dynamic normals of each constraint point of the over-constrained component is: A: When the static normals of each constraint point of the over-constrained component intersect at one point, if each constraint point can If the angular velocities are equal, then the velocities match; B: If the static normals at each constraint point of the over-constrained member are parallel to each other, if the linear velocities at each constraint point have the same direction and the same magnitude, then the velocity matches.
进一步的，根据过约束构件各约束点的动法线的速度匹配的方法判断构件受到约束的类别的方法为：过约束构件只能在某一瞬间满足A、B两个条件，机构中各构件的位置改变后，即不能满足A、B两个条件，则该构件为瞬时虚约束；过约束构件时刻能满足A、B两个条件，则该构件为虚约束；过约束构件任何时刻都不能满足A、B两个条件，则该构件为实约束。Further, according to the speed matching method of the dynamic normal of each constraint point of the over-constrained component, the method for judging the category of the component constrained is as follows: the over-constrained component can only meet the two conditions A and B at a certain moment, and each component in the mechanism After the change of the position of , that is, the two conditions A and B cannot be satisfied, the component is an instantaneous virtual constraint; the over-constrained component can satisfy the two conditions A and B at any time, then the component is a virtual constraint; the over-constrained component cannot be If the two conditions of A and B are met, the component is a real constraint.
本发明的有益效果：本发明不仅将机构整体受到的虚约束具体到某些构件的虚约束，而且可以得到虚约束构件具体存在几个虚约束，采用约束法线的方法，在分析机构虚约束的过程中更加简单、直观、通用，不需要高深的理论基础和复杂的数学计算，使相关工作人员更易于接受使用，也更加易于推广，可广泛应用于创造机构，分析机构，改进机构及对机构的研究。Beneficial effects of the present invention: the present invention not only specifies the virtual constraints received by the whole mechanism to the virtual constraints of certain components, but also can obtain several virtual constraints that exist in the virtual constrained components. The process is simpler, intuitive, and universal, and does not require advanced theoretical foundations and complex mathematical calculations, making it easier for relevant staff to accept and use, and easier to promote. It can be widely used in creating institutions, analyzing institutions, improving institutions, and improving institutions. Institutional research.
附图说明Description of drawings
图1是发明判断机构虚约束的框架图；Fig. 1 is a frame diagram of the virtual constraints of the inventive judging mechanism;
图2为实施例中平面多平行四边形机构中虚约束的示意图。Fig. 2 is a schematic diagram of virtual constraints in the planar multi-parallelogram mechanism in the embodiment.
具体实施方式Detailed ways
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.
一种基于约束法线判断机构虚约束的方法，具体包括以下步骤：A method for judging a virtual constraint of a mechanism based on a constraint normal, specifically comprising the following steps:
（1）将机构中各个运动副均等效成若干个约束点，将约束点处的法线定义为约束法线，所述约束法线分为静法线、动法线、冗余法线，并将各个运动副的静法线、动法线标示出来，所述静法线为两构件之间瞬时相对速度为零的法线，所述动法线为与静法线垂直的法线，所述冗余法线为重复约束某自由度的静法线；(1) Each kinematic pair in the mechanism is equivalent to several constraint points, and the normal at the constraint point is defined as the constraint normal. The constraint normal is divided into static normal, dynamic normal, and redundant normal. And mark the static normal and dynamic normal of each kinematic pair, the static normal is the normal of the instantaneous relative velocity between the two members, and the dynamic normal is the normal perpendicular to the static normal, The redundant normal is a static normal repeatedly constrained to a certain degree of freedom;
（2）将机构中的构件分为同根构件和母体构件，所述母体构件是指可与机构中的几个构件形成运动副的构件，所述几个构件即为一组同根构件；(2) Divide the components in the mechanism into the same root component and the parent component, the parent component refers to a component that can form a kinematic pair with several components in the mechanism, and the several components are a group of common root components;
（3）根据构件各约束点静法线的数量及其几何关系建立判断构件过约束的几何方法，以判断构件是否受到过约束，如果构件不过约束则该构件不存在虚约束，如果该构件存在过约束的情况，则根据该构件各约束点的动法线的速度是否时刻匹配，进而判断构件受到约束的类别，所述约束的类别分为实约束、瞬时虚约束和虚约束。(3) According to the number of static normals of each constraint point of the component and its geometric relationship, a geometric method for judging the over-constraint of the component is established to determine whether the component is over-constrained. If the component is not over-constrained, the component does not have virtual constraints. If the component exists In the case of over-constraint, according to whether the velocity of the dynamic normal of each constraint point of the component matches at all times, and then judge the category of the component constrained, the category of constraints is divided into real constraints, instantaneous virtual constraints and virtual constraints.
步骤（3）中根据构件各约束点静法线的数量及其几何关系建立判断构件过约束的方法为：In step (3), the method for judging the over-constraint of a component is established according to the number of static normal lines of each constraint point of the component and its geometric relationship:
a：非同根构件判断过约束的方法：机构中的一组同根构件同时约束甲构件，且甲构件各约束点处同交于一点的有效法线数量或相互平行的有效法线数量nh大于法线所在空间的维度d时，则甲构件过约束且冗余法线的数量为nh-d；同理，机构中有h组同根构件同时约束甲构件，且各组构件对甲构件同交于一点的有效法线数量或各组相互平行的有效法线数量nh大于d+h-1时，则甲构件过约束且冗余法线的数量为nh-h-d+1；a: The method for judging over-constraint by non-same-rooted components: A group of components with the same root in the mechanism constrains member A at the same time, and the number of effective normals co-intersecting at one point at each constraint point of member A or the number n h of effective normals parallel to each other is greater than When the dimension of the space where the normal line is located is d, the A component is over-constrained and the number of redundant normals is n h -d; similarly, there are h groups of components with the same root constraining the A component at the same time in the mechanism, and each group of components has the same effect on the A component. When the number of effective normals intersecting at one point or the number n h of effective normals parallel to each other is greater than d+h-1, the A member is over-constrained and the number of redundant normals is n h -h-d+1;
b：同根构件判断过约束的方法：机构中有一组同根构件两两相互约束或一组同根构件两两直接约束其它多个构件时，若某同根构件有效法线数量nh在空间内大于6、平面内大于3时，则该构件过约束，且该构件的冗余法线数量在空间内为nh-6，在平面内为nh-3，机构中冗余法线的总数量为各构件冗余法线数量之和。b: The method for judging over-constraint of the same-root component: when there is a group of same-root components pairwise constraining each other in the mechanism or a group of same-root components directly constraining other multiple components, if the effective normal number n h of a certain same-root component is greater than 6 in the space , when the in-plane is greater than 3, the component is over-constrained, and the number of redundant normals of the component is n h -6 in space, n h -3 in the plane, and the total number of redundant normals in the mechanism is The sum of the number of redundant normals of each component.
所述有效法线的定义为：乙构件对甲构件的静法线及甲构件对丙构件的静法线统称为甲构件的有效法线。The effective normal is defined as follows: the static normal of component B to component A and the static normal of component A to component C are collectively referred to as the effective normal of component A.
步骤（3）中判断过约束构件各约束点的动法线的速度匹配的方法为：A：当过约束构件各约束点处的静法线交于一点时，若各约束点能够保证角速度相等则速度匹配；B：若过约束构件各约束点处的静法线相互平行时，若各约束点线速度方向相同大小相等则速度匹配。根据过约束构件各约束点的动法线的速度匹配的方法判断构件受到约束的类别的方法为：过约束构件只能在某一瞬间满足A、B两个条件，机构中各构件的位置改变后，即不能满足A、B两个条件，则该构件为瞬时虚约束；过约束构件时刻能满足A、B两个条件，则该构件为虚约束；过约束构件任何时刻都不能满足A、B两个条件，则该构件为实约束。The method for judging the velocity matching of the dynamic normal of each constraint point of the over-constrained component in step (3) is: A: When the static normals of each constraint point of the over-constrained component intersect at one point, if each constraint point can guarantee the same angular velocity Then the velocity matches; B: If the static normals at each constraint point of the over-constrained member are parallel to each other, if the line velocity direction of each constraint point is the same and the magnitude is equal, then the velocity matches. According to the speed matching method of the dynamic normal line of each constraint point of the over-constrained component, the method of judging the type of component constrained is as follows: the over-constrained component can only meet the two conditions A and B at a certain moment, and the position of each component in the mechanism changes If the two conditions A and B cannot be satisfied, the component is an instantaneous virtual constraint; the over-constrained component can satisfy the two conditions A and B at any time, then the component is a virtual constraint; the over-constrained component cannot satisfy A, B at any time B two conditions, then the component is a real constraint.
参照图1所示，本实施例以平面多平行四边形机构中的虚约束来说明，如图2 平面多平行四边形机构，构件1为主动件。首先将机构中转动副B、E、G、C等效成点约束，并将这些转动副的约束法线分别表示为转动副B静法线Fj15、动法线Fd15，其余转动副的动静法线如图中所示，其次分析机构中各构件所受到的静法线的数量及几何关系。其中构件1受到机架的两条相互垂直的有效法线，并且给构件5一条沿构件1方向的一条有效法线，这三条法线在机构所在的平面内既不相交于一点，也不相互平行，因此构件1不过约束，更不存在虚约束。构件5受到构件1的一条沿构件1方向的一条有效法线，同时对构件2、3、4各有一条沿构件2、3、4方向的有效法线，由于构件5的4条有效法线相互平行，因此构件5过约束；同时构件1、2、3、4相等且平行，因此构件5的动法线方向相同且速度大小相等，而平面内任何一个构件受到4条相互平行的有效法线，且速度大小相等必然虚约束，构件1、2、3、4为一组同根构件同时约束构件5，h=1。机构冗余法线数量为nr=nh-h-d+1=4-1-2+1=2，因此构件5受到2个虚约束，显然该虚约束非瞬时虚约束。构件2、3、4所受到的有效约束法线与构件1类似，因此不存在虚约束。Referring to Fig. 1, this embodiment is illustrated by the virtual constraints in the planar multi-parallelogram mechanism, as shown in Fig. 2, the planar multi-parallelogram mechanism, component 1 is the active part. First, the revolving pairs B, E, G, and C in the mechanism are equivalent to point constraints, and the constrained normals of these revolving pairs are denoted as the static normal F j15 of revolving pair B and the dynamic normal F d15 of revolving pairs respectively, and the other revolving pairs The dynamic and static normals are shown in the figure, and then analyze the quantity and geometric relationship of the static normals received by each component in the mechanism. Among them, component 1 receives two mutually perpendicular effective normal lines of the frame, and gives component 5 an effective normal line along the direction of component 1. These three normal lines neither intersect at one point in the plane where the mechanism is located, nor intersect each other. Parallel, so component 1 is not constrained, let alone virtual constraints. Component 5 receives an effective normal of component 1 along the direction of component 1, and at the same time, there is an effective normal of component 2, 3, and 4 along the direction of component 2, 3, and 4. Since the four effective normals of component 5 are parallel to each other, so component 5 is over-constrained; at the same time, components 1, 2, 3, and 4 are equal and parallel, so the dynamic normal direction of component 5 is the same and the velocity is equal, and any component in the plane is subject to four effective normals parallel to each other. Lines, and equal velocity must be virtual constraints, members 1, 2, 3, 4 are a group of members with the same root and constrain member 5 at the same time, h=1. The number of redundant normals of the mechanism is n r =n h -h-d+1=4-1-2+1=2, so member 5 is subject to two virtual constraints, which are obviously not instantaneous virtual constraints. The effective constrained normals of components 2, 3, and 4 are similar to those of component 1, so there is no virtual constraint.
最后应说明的是：以上所述仅为本发明的实施例而已，用于解释本发明，并不用于限制本发明，尽管参照前述实施例对本发明进行了详细的说明，对于本领域的技术人员来说，其依然可以对前述各实施例所记载的技术方案进行修改，或者对其中部分技术特征进行等同替换。凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。Finally, it should be noted that: the above is only an embodiment of the present invention, and is used to explain the present invention, and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, for those skilled in the art However, it is still possible to modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.
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