摘要
在评价人工髋关节生物材料摩擦磨损特性以及验证其理论计算结果与实际应用的吻合程度时往往需进行摩擦学试验。而摩擦学试验结果在很大程度上受试验设备影响。因此,所选用试验机应能模拟关节副实际工况条件,构造出与人体髋关节摩擦情况类似的摩擦实验环境。本文选用了并联仿生模块作为髋关节试验机的主体运动部分。由于须模拟实际人体髋关节的生物环境,不但其运动学性能要满足关节臼与关节球之间的相对运动特性,而且其承载能力也要符合关节之间快速变化载荷的要求。因此,并联仿生模块的选择必须满足三个转动自由度的运动要求以及一个平动自由度的加载动力要求,考虑到机构运动与动力特性求解、研制成本等原因,本项目中并联仿生模块选择1移动3转动的四自由度并联模块。为了使所研制的并联模块具有优异的仿生运动与动力性能,需要从并联仿生模块的构型综合、运动学分析、奇异位形求解、工作空间优化等关键技术分别进行研究,最后研制出一台3SPS+1PS型髋关节并联仿生试验样机。本文主要研究内容如下:
随机抽取了20位试验者对实际人体髋关节生物特性进行试验分析。通过OptotrakCertus运动系统对试验者的各种步态动作的三维运动学参数进行捕捉采集,并建立参数的三维模型。通过对运动学参数的统计学研究,为并联式髋关节试验机轨迹规划提供了实验数据。
采用四元素参数对以3SPS+1PS型对称并联机构为核心的髋关节试验机进行运动学建模,并且描述了机构的空间位姿,建立了机构位移逆/正方程、速度逆/正方程,加速度逆/正方程及Jacobi矩阵。根据实际人体髋关节运动步态轨迹,规划了该机构动平台的运动轨迹。由机构逆运动学方程求得各支链驱动杆的位移、速度及加速度变化曲线,根据所得数值结果给各驱动杆赋值可实现所规划的动平台轨迹。
针对3SPS+1PS并联机构,建立了该机构支链与动平台的静力学平衡方程,由机构静态力学转换矩阵P的plǜcker坐标表达式得到六条空间分析直线,通过该六条直线之间的线性相关性可对该机构奇异位形进行研究。基于Grassmann几何理论,从奇异位形的空间几何本质入手,得到该机构的线簇秩1到5的32种奇异位形。其中低秩奇异位形较多也较复杂,但其空间几何分布易于理解,奇异曲面和奇异曲线的表达式较简单,在轨迹规划时,不会造成多大的困难。高秩奇异位形简单对机构的运动轨迹规划非常有利。
基于四元数法描述了3SPS+1PS并联仿生试验平台的位姿,提出了该并联仿生试验平台的机构无量纲Jacobi矩阵。根据四元数和Euler角的转换关系,将动平台姿态空间数值结果集合用Euler角参数在三维坐标中可视化表示,既避免了用Euler角描述动平台的位姿时出现的奇异问题,又使姿态空间表达地更直观。分析并仿真了该机构的可达姿态工作空间,得到了姿态运动空间的优化结构参数。将机构无量纲Jacobi矩阵条件数允许值取为15~20范围内作为约束条件,得到了较大体积的灵活姿态空间。进一步约束无量纲Jacobi矩阵条件数允许值及其奇异值取值范围,得到了在运动空间内机构允许运动速度及控制精度。
采用UG NX建立机构三维模型,利用ADAMS进行运动学和动力学仿真,求解出3SPS+1PS四自由度并联机构正解和逆解。基于UG建立的机构三维模型,根据逆运动学求解并模拟了该机构动平台绕定坐标系各轴的6个转动极值时的位姿情况,可得机构能够实现模拟人体髋关节的运动空间。在验证机构运动正确性的基础上,根据实际人体髋关节的生物特性,在机构动平台上施加一外载荷,利用反解求得其运动规律,然后进行机构的动力学仿真分析。通过ANSYS对其在不同载荷情况下整体静力学、动力学进行了分析,确定了机构的应力应变、固有频率及振型,避免了机构运动时与固有频率相近振源的干扰。
根据前述的运动学与动力学分析结果,制定了机构的总体设计方案,并结合试验机的设计要求,对机构在机械加工与装配过程中进行了详细设计,研制了髋关节试验机的样机。建立了以工控机、控制柜、电动缸和液压加载模块为核心的系统控制结构,采用了批量传递为辅、先置轨迹规划为主的数据传递模式,有效的减少了数据传递量,提高了系统的稳定性,加快了系统响应速度。最后,并对实验系统的机械结构以及控制方式等方面提出了改进意见。
In order to evaluate friction and wear characteristics of hip joint prosthesis biomaterials as well as to verify the coincidence between its theoretical results and test results, a tribology test for the biomaterials is primarily important. However, the accuracy of the tribology test largely depends on test simulators. Therefore, the hip joint simulators intend to simulate the actual working conditions of the human hip joint. In this dissertation, as the key component of a novel hip joint simulator, a bionic parallel mechanism is proposed. The hip joint simulator should provide the movement and dynamic alternating load between the joint and acetabular. Therefore, the parallel mechanism should at least have three rotations movement and one translation which produces load, i.e. the degree of freedoms of the bionic parallel mechanism are more than or equal to 4. Moreover, taking kinematic and dynamic performance of the mechanism and its manufacture cast into consideration, the degree of freedoms of the bionic parallel mechanism are set as 4, i.e. 4-DOF parallel mechanism which has one translation and three rotations. In order to make sure the parallel mechanism can accurately represent bionic motion and dynamic, it need to analyze the mechanism type- synthesis, kinematics, singular configurations, and workspace optimization, and so on. Finally, a 3SPS+1PS bionic parallel mechanism as a novel hip joint simulator is developed. The main study works in this paper are as follows:
20 healthy young adults are randomly recruited for gait analysis of the human hip joint. 3D movement kinematics parameters of all kinds of gait are captured using an Optotrak Certus motion capture system, and then used to create a model from which kinematics is determined. Through the statistically analysis of the interested kinematic variables, experimental data are obtained for planning trajectory of the parallel hip joint test mechanism.
Based on the quaternion method, the kinematic model of the 3SPS+1PS parallel mechanism is built, the position/orientation is depicted, and the inverse/forward displacement kinematics, inverse/forward velocity, inverse/forward acceleration and Jacobi matrix are derived. According to the gait trajectory of the human hip joint, trajectory of the moving platform of the 3SPS+1PS parallel mechanism is planned. Based on inverse kinematics analysis, the corresponding displacement, velocity and acceleration carves of the active legs are derived. Therefore, the parallel mechanism can represent the planned trajectory by driving the active legs with their inverse numerical data.
For the 3SPS+1PS bionic parallel mechanism, the static mechanics of the mechanism is analyzed, and the static mechanics conversion matrix P is obtained. Six matrix column vectors can be presented by six Plücker vectors which associate with six analytical lines for Grassmann analysis. The analysis of the forward singularities by studying the linear dependency of six analytical lines using Grassmann geometry yielded to 32 singular configurations. The lower rank singular configurations are rich and complex, but their distributions are easily understood and their singular surfaces or carves are simple enough to plan the trajectory of the parallel mechanism. And the simple higher rank singular configurations are advantage for planning trajectory.
For the 3SPS+1PS bionic parallel mechanism, the inverse position/orientation equations and the corresponding dimensionally Jacobi matrix are derived based on the quaternion method. In order to avoid the singularities caused by Euler angles and allow the orientation workspace to be depicted intuitively, the sets of the three-dimensional orientation workspace of the parallel manipulator are clearly depicted by Euler angles according to the relationship between the quaternion and Euler angles. By simulating the corresponding reachable orientation workspace with different architectures, the optimized architectures are derived. In addition, the workspace volume largely depends on the permissible rotation angles of spherical joints, particularly the permissible rotation angle of the spherical joints on the moving platform. In order to obtain a larger and well-conditioned orientation workspace, the maximum permissible condition numbers of the Jacobi matrix are set as 15~20. Regions of the dexterous orientation workspaces corresponding to the Jacobi matrix singular values, where either high output velocities may be achieved or where fine accuracy over the manipulator orientation exists are derived by constraining the Jacobi matrix condition number and its singular value.
The 3D model of the 3SPS+1PS bionic parallel mechanism is conducted in UG NX. And inverse/forward kinematics of the parallel mechanism is simulated in ADAMS. To prove the numerical results, six extreme motions of the simulation manipulator are conducted in UG NX. From the simulating results, it can be derived that the 3SPS+1PS bionic parallel mechanism can produce enough workspace for simulating gait movement of the human hip joint. After verifying the correctness of the parallel mechanism’s kinematics, dynamic of the mechanism is analyzed by loading a force on the moving platform. Statics and dynamics performance of the parallel mechanism are analyzed based on ANSYS. Stress and strain, natural frequency and vibration modes of the parallel mechanism are derived. This can make sure parallel mechanism avoids the interference of vibration source which frequency closes to the parallel mechanism’s natural frequency.
The general design scheme is derived based on the previous kinematics and dynamics analysis. And combining with the design requirements of the hip joint simulator, a prototype mechanism of the hip joint simulator is developed by designing machining and agency processes of the mechanism in detail. The key parts of control system include computer, control cabinet, electric cylinder and hydraulic loading modularity. With the based trajectory and the supplemented bulk transfer, the method of data transmission improves stability and expedited the response velocity of system. Finally, some suggestions are proposed for the mechanical structure and control.
引文
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