基于CAD变量几何法并联机床加工复杂曲面的关键技术研究
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摘要
近几十年来,并联机构成为国际上研究的热点,而其在工业上的重要应用是用作并联机床。并联机床作为一类全新结构的机床,与传统的数控机床形成很强的互补,而对于并联机床加工复杂型曲面中关键技术的研究,属于并联机构学和机床加工工艺领域。随着工业生产的发展,并联机床在实际应用中显得日趋重要,而对于并联机构学领域的基础理论研究方法还有待于进一步完善。本文以CAD变量几何为研究方法,以解决任意并联机床在加工复杂型曲面过程中,其关键机构的运动学、静力学等关键问题为出发点,主要包括以下几个方面:
基于CAD变量几何,建立并联机器人加工复杂轨迹和复杂型曲面的统一模拟机构,用以求解加工过程中,因难以建立复杂曲线和曲面的解析方程,而无法确定的并联机器人各输入驱动参数。以三维移动3-UPRR、新型非对称3-UPU并联机构,以及具有中间驱动分支的新型少腿5自由度3SPS+RRPU并联机床为研究对象,分别以往复直线、螺旋线以及复杂字母曲线为加工轨迹,阐述模拟机构的建立方法,并建立了5自由度3SPS+RRPU并联机床法向加工的模型。
基于CAD变量几何求解并联机构的运动学。将欧拉角引入到CAD变量几何中,以有限差分理论为数学基础,建立求解并联机构位置、姿态、线速度/线加速度、欧拉角速度/角加速度的统一方法。提出一种新型三腿5自由度2SPS+RRPRR并联机床,以其和经典的3/6-SPS型并联机构为研究对象,求解其运动学参数的精确值。为解决并联机床加工复杂曲面过程中的速度、加速度问题奠定了理论基础与研究方法。
基于CAD变量几何,从虚功原理和力/力矩平衡方程两种思路,求解并联机构的驱动力与约束力/力矩。在基于虚功原理的方法中,归纳出三点关键性结论,并给出理论证明,分别以3-RPS和2SPS+2UPU并联机构为例,阐述基于虚功原理的求解方法;分别以只含有约束力的对称3UPUⅠ型、只含有约束力矩的非对称3UPUⅡ型并联机构为例,阐述基于力/力矩平衡方程的求解方法。为求解并联机床加工复杂曲面过程中的驱动力问题奠定了研究方法。
综合上述所有的研究方法并基于CAD变量几何,求解并联机床法向加工任意复杂曲面过程中的速度、加速度、驱动力等关键问题。对于难以建立解析方程的空间复杂型自由曲面,以新型5自由度4SPS+SPR并联机床为研究对象,构造其法向加工的模拟加工系统,根据预定的轨迹和加工速度要求,预先求解出整个加工过程所需的各驱动输入参数,以及驱动杆和末端平台的速度、加速度变化参数,确定加工中的奇异位形或速度、加速度突变的位置,通过修改运动学参数,避免这些问题的出现,保证加工质量;并分析了两种轨迹下驱动力的变化情况,用以选择合适的加工路径。
对5自由度4SPS+SPR并联机床建立了解析模型。推导求解其位移、速度、加速度及驱动力/约束力的解析方程,得到其含有约束力在内的6×6 Jacobian矩阵及Hessian矩阵。研究该并联机床位置正解的封闭解,提出5自由度并联机构具有56组正解,并与CAD变量几何法求得的位置正解相互验证。
基于CAD变量几何法和现有可重组实验台,调试出一系列具有中间约束分支的新型3自由度2SPS+UPU/SP并联机构。通过对其自由度性质的分析,得出该系列并联机构随运动副布置方向的不同具有3转和2转1移的自由度,建立该系列并联机构运动学和静力学的统一方程式。以具有2转1移自由度的构型为基础,基于模块化并联机构试验平台,开发新型并联样机,基于该样机的控制系统和Windows平台的控制软件,通过CAD变量几何法进行数据的采集,使并联样机末端实现预定轨迹的描绘,用以验证CAD变量几何法研究并联机床以及并联机构的正确性。
Nowadays, parallel manipulator (PM) is becoming more and more popular in the field of robotic research. And parallel machine tool (PMT) is an important application in industry. PMT, as a new-style machine tool, complements the traditional NC machine tool perfectly. The research of the basal theory of PMT is a part of the area of PM and machine tool studies. With the development of the industry, PMTs are becoming more and more important in actual applications. A further study of the basal theory on the PMTs is needed. This paper starts with the key problems in the process of machining complicated surface which are unable to establish the analytic equations, the main contributions are as follows:
Based on CAD variation geometry approach, the uniform model of machining a general complicated surface by parallel robots is founded to solve all the input driving parameters in the process. The 3-UPRR and the novel unsymmetrical 3-UPU PMs with 3 translation degrees of freedom (dofs), and the novel 5 dofs 3SPS+RRPU PMT with middle driving limb are proposed. Three paths of straight-line, spiral and special letter curves are adopted, and the constitution method is expounded. And the model for normal machining by a 5 dofs PMT 3SPS+RRPU is founded.
CAD variation geometry approach is proposed to solve the kinematics of PMs. The Euler angles are introduced into the CAD variation geometry. Based on the finite-differential theory, a unified method is proposed for solving the position-orientation, linear velocity/ acceleration, and Euler angular velocity/ acceleration. A novel 5 dofs 2SPS+RRPRR PM with 3 limbs is put forward. Based on the 2SPS+RRPRR and the classical 3/6-SPS PMs, the accurate solutions of the kinematics are solved. It lays a theoretical foundation and provides a method for solving the velocity and acceleration in the process of machining a complicated surface.
Based on the CAD variation geometry, the active forces and constrained forces of any PM are solved from two aspects of the principle of virtual work and the static balance equations. Three pivotal conclusions are induced and verified for the case of using the principle of virtual work. The first method is introduced with 3-RPS and 2SPS+2UPU PMs as examples; and the second method is explained with the 3UPUⅠPM containing only the constrained forces and 3UPUⅡPM containing only the constrained torques as examples.
Synthesizing all the methods above, it is suggested that the CAD variation geometry should be introduced to solve the key problems in machining a surface. For the complicated surface which is hard to establish the math equations, the normal simulation machine system is constructed based on the 5-dof 4SPS+SPR PMT. All of the input parameters in the whole machining process are solved according to the expectant tool path and machining velocity. The kinematics and statics are analyzed in advance, and the singularity or the shape point of the kinematics is found. By modification of the kinematics parameters, these positions can be avoided and the machine quality can be ensured. The driving forces along the two paths are analyzed in order to choose an appropriate curve.
The analytic model of the novel 5-dof 4SPS+SPR PMT is established, and the analytic equations for solving the velocity, acceleration and statics are derived. The 6×6 Jacobian matrix and Hessian matrix are obtained. The forward position of the PMT is analyzed, and it is claimed that the 5-dof PMT has 56 groups of solutions. The analytic solutions are validated by the CAD variation geometry approach.
Based on the CAD variation geometry approach and the existing test-bed, a series of 3-dof 2SPS+UPU/SP PMs with the constrained leg are put forward. By analyzing the properties of their dofs, it is found that the 2SPS+UPU/SP PMs have two kinds of dofs: 3 translations; and 2 rotations plus 1 translation. Then the uniform analytic equations for solving the kinematics and statics are established. Taking the novel 2SPS+UPU/SP PM with the 2 rotations and 1 translation as the prototype, and based on the modularization test-bed of PM, the novel sample machine is exploited. Based on Windows Operating System and data collection by CAD variation geometry approach, the expectant track is painted by the sample machine in order to prove the validity of CAD variation geometry approach.
基于CAD变量几何,建立并联机器人加工复杂轨迹和复杂型曲面的统一模拟机构,用以求解加工过程中,因难以建立复杂曲线和曲面的解析方程,而无法确定的并联机器人各输入驱动参数。以三维移动3-UPRR、新型非对称3-UPU并联机构,以及具有中间驱动分支的新型少腿5自由度3SPS+RRPU并联机床为研究对象,分别以往复直线、螺旋线以及复杂字母曲线为加工轨迹,阐述模拟机构的建立方法,并建立了5自由度3SPS+RRPU并联机床法向加工的模型。
基于CAD变量几何求解并联机构的运动学。将欧拉角引入到CAD变量几何中,以有限差分理论为数学基础,建立求解并联机构位置、姿态、线速度/线加速度、欧拉角速度/角加速度的统一方法。提出一种新型三腿5自由度2SPS+RRPRR并联机床,以其和经典的3/6-SPS型并联机构为研究对象,求解其运动学参数的精确值。为解决并联机床加工复杂曲面过程中的速度、加速度问题奠定了理论基础与研究方法。
基于CAD变量几何,从虚功原理和力/力矩平衡方程两种思路,求解并联机构的驱动力与约束力/力矩。在基于虚功原理的方法中,归纳出三点关键性结论,并给出理论证明,分别以3-RPS和2SPS+2UPU并联机构为例,阐述基于虚功原理的求解方法;分别以只含有约束力的对称3UPUⅠ型、只含有约束力矩的非对称3UPUⅡ型并联机构为例,阐述基于力/力矩平衡方程的求解方法。为求解并联机床加工复杂曲面过程中的驱动力问题奠定了研究方法。
综合上述所有的研究方法并基于CAD变量几何,求解并联机床法向加工任意复杂曲面过程中的速度、加速度、驱动力等关键问题。对于难以建立解析方程的空间复杂型自由曲面,以新型5自由度4SPS+SPR并联机床为研究对象,构造其法向加工的模拟加工系统,根据预定的轨迹和加工速度要求,预先求解出整个加工过程所需的各驱动输入参数,以及驱动杆和末端平台的速度、加速度变化参数,确定加工中的奇异位形或速度、加速度突变的位置,通过修改运动学参数,避免这些问题的出现,保证加工质量;并分析了两种轨迹下驱动力的变化情况,用以选择合适的加工路径。
对5自由度4SPS+SPR并联机床建立了解析模型。推导求解其位移、速度、加速度及驱动力/约束力的解析方程,得到其含有约束力在内的6×6 Jacobian矩阵及Hessian矩阵。研究该并联机床位置正解的封闭解,提出5自由度并联机构具有56组正解,并与CAD变量几何法求得的位置正解相互验证。
基于CAD变量几何法和现有可重组实验台,调试出一系列具有中间约束分支的新型3自由度2SPS+UPU/SP并联机构。通过对其自由度性质的分析,得出该系列并联机构随运动副布置方向的不同具有3转和2转1移的自由度,建立该系列并联机构运动学和静力学的统一方程式。以具有2转1移自由度的构型为基础,基于模块化并联机构试验平台,开发新型并联样机,基于该样机的控制系统和Windows平台的控制软件,通过CAD变量几何法进行数据的采集,使并联样机末端实现预定轨迹的描绘,用以验证CAD变量几何法研究并联机床以及并联机构的正确性。
Nowadays, parallel manipulator (PM) is becoming more and more popular in the field of robotic research. And parallel machine tool (PMT) is an important application in industry. PMT, as a new-style machine tool, complements the traditional NC machine tool perfectly. The research of the basal theory of PMT is a part of the area of PM and machine tool studies. With the development of the industry, PMTs are becoming more and more important in actual applications. A further study of the basal theory on the PMTs is needed. This paper starts with the key problems in the process of machining complicated surface which are unable to establish the analytic equations, the main contributions are as follows:
Based on CAD variation geometry approach, the uniform model of machining a general complicated surface by parallel robots is founded to solve all the input driving parameters in the process. The 3-UPRR and the novel unsymmetrical 3-UPU PMs with 3 translation degrees of freedom (dofs), and the novel 5 dofs 3SPS+RRPU PMT with middle driving limb are proposed. Three paths of straight-line, spiral and special letter curves are adopted, and the constitution method is expounded. And the model for normal machining by a 5 dofs PMT 3SPS+RRPU is founded.
CAD variation geometry approach is proposed to solve the kinematics of PMs. The Euler angles are introduced into the CAD variation geometry. Based on the finite-differential theory, a unified method is proposed for solving the position-orientation, linear velocity/ acceleration, and Euler angular velocity/ acceleration. A novel 5 dofs 2SPS+RRPRR PM with 3 limbs is put forward. Based on the 2SPS+RRPRR and the classical 3/6-SPS PMs, the accurate solutions of the kinematics are solved. It lays a theoretical foundation and provides a method for solving the velocity and acceleration in the process of machining a complicated surface.
Based on the CAD variation geometry, the active forces and constrained forces of any PM are solved from two aspects of the principle of virtual work and the static balance equations. Three pivotal conclusions are induced and verified for the case of using the principle of virtual work. The first method is introduced with 3-RPS and 2SPS+2UPU PMs as examples; and the second method is explained with the 3UPUⅠPM containing only the constrained forces and 3UPUⅡPM containing only the constrained torques as examples.
Synthesizing all the methods above, it is suggested that the CAD variation geometry should be introduced to solve the key problems in machining a surface. For the complicated surface which is hard to establish the math equations, the normal simulation machine system is constructed based on the 5-dof 4SPS+SPR PMT. All of the input parameters in the whole machining process are solved according to the expectant tool path and machining velocity. The kinematics and statics are analyzed in advance, and the singularity or the shape point of the kinematics is found. By modification of the kinematics parameters, these positions can be avoided and the machine quality can be ensured. The driving forces along the two paths are analyzed in order to choose an appropriate curve.
The analytic model of the novel 5-dof 4SPS+SPR PMT is established, and the analytic equations for solving the velocity, acceleration and statics are derived. The 6×6 Jacobian matrix and Hessian matrix are obtained. The forward position of the PMT is analyzed, and it is claimed that the 5-dof PMT has 56 groups of solutions. The analytic solutions are validated by the CAD variation geometry approach.
Based on the CAD variation geometry approach and the existing test-bed, a series of 3-dof 2SPS+UPU/SP PMs with the constrained leg are put forward. By analyzing the properties of their dofs, it is found that the 2SPS+UPU/SP PMs have two kinds of dofs: 3 translations; and 2 rotations plus 1 translation. Then the uniform analytic equations for solving the kinematics and statics are established. Taking the novel 2SPS+UPU/SP PM with the 2 rotations and 1 translation as the prototype, and based on the modularization test-bed of PM, the novel sample machine is exploited. Based on Windows Operating System and data collection by CAD variation geometry approach, the expectant track is painted by the sample machine in order to prove the validity of CAD variation geometry approach.
引文
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