基于并联机构的六维加速度传感器的方案设计及建模研究

提出一种新的基于并联机构的压电式六维加速度传感器的设计方案,即用并联机构充当传感器的弹性体结构,压电陶瓷同时充当传感器的敏感元件和并联机构的移动副,弹性球铰链代替传统的球面副.分别在质量块、外壳及地面上固结坐标系,基于多体系统理论推导两两之间位姿关系的解析表达式.运用牛顿-欧拉法建立系统的动力学方程,通过引入辅助角速度并用四元数来描述旋转矩阵和角速度矢量,将其转化成两个一阶常微分方程组的初值问题,并运用改进的欧拉算法进行求解,实现了六维加速度的完全解耦.针对四元数的违约问题,运用矩阵广义逆理论提出了一种有效的可重复运行的修正算法.利用建立的解耦模型及其算法对实例进行了求解,数据处理总时间小于采样点时间跨度,且理论计算值与ADAMS仿真数据吻合得很好；另外,通过试验进一步验证了设计方案的合理性以及数学模型的可靠性.

The Scheme design and modeling research of Six-axis Accelerometer Based on Parallel Mechanism

Six-axis accelerometer is a kind of inertial sensors getting kinetic parameters in the field of aerospace, robots and the like, and researches on it at home and abroad are still at exploring stage. A new scheme of using parallel mechanism as plastic structure and piezoelectric ceramic as sensitive element of the transducer is presented. Piezoelectric ceramic is also used to serve as prismatic pair of parallel mechanism and traditional spherical pair is replaced by flexure spherical hinge. Three coordinates are consolidated at mass-block, shell and ground respectively, and their relationships of position and pose are established according to the theory of multi-body system. Based on Newton-Euler method, the dynamic equation of the system is established, and the problem is transformed into two initial value problems of first-order ordinary differential equations, which are solved by improved Euler method, by introducing aided angular velocity and using quaternions to describe rotation matrix and angular velocity, and accelerations are decoupled. Method of generalized inverse for matrix is used to treat the violated constraint problem of quaternion. Based on the established mathematical model, a numerical example is computed. The result is contrasted with the simulation result in ADAMS, and the relative error between them is acceptable. Meanwhile, time of data processing is no more than that of sampling. At last, the experiment is done, which shows that the new sensor can be used to measure six-axis acceleration real-timely and accurately.