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首页> 外文期刊>IEEE / ASME Transactions on Mechatronics >Discrete Deformation Models for Real-Time Computation of Compliant Mechanisms in Two- and Three-Dimensional Space
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Discrete Deformation Models for Real-Time Computation of Compliant Mechanisms in Two- and Three-Dimensional Space

机译：二维和三维空间中柔顺机构实时计算的离散变形模型

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摘要

Motivated by the need to develop a real-time computation method for simultaneous real-time visualization and force/torque feedback for manipulating of compliant mechanisms, this paper presents a general formulation of a reduced-order discrete state space model and its solution as a function of path lengths for a three-dimensional (3-D) curvature-based beam model (CBM). Unlike a compliant beam model where the boundary value problem is solved using a shooting method, the state-space representation decouples the 13th order CBM into two sets of reduced-order ordinary differential equations; the first solves for the orientation and moment whereas the second describes the deformed beam shape. Thus, it enables parallel computation of the deformed shape from the solutions to the orientation and moments. As illustrative examples, the state-space formulation and real-time computation method have been applied to analyze two flexure-based mobile-sensing node (FMN) designs. The new design, which overcomes several kinematic limitations and practical implementation problems commonly encountered in FMN navigation in tight 3-D space, permits bending and twisting of the compliant beam in 3-D space. The discrete linear CBM for the two FMN designs has been validated experimentally as well as verified by comparing computed results against published data and simulations using multishooting method and finite-element analysis.
机译：由于需要开发一种实时计算方法以同时进行实时可视化和力/转矩反馈以操纵顺应机构，本论文提出了降阶离散状态空间模型的一般表示及其作为函数的解决方案三维（3-D）基于曲率的波束模型（CBM）的路径长度的示意图。与使用射击方法解决边值问题的顺应光束模型不同，状态空间表示将13阶CBM解耦为两组降阶常微分方程。第一个求解方向和力矩，而第二个描述变形的光束形状。因此，它能够从方向和力矩的解中并行计算变形形状。作为说明性示例，状态空间公式化和实时计算方法已应用于分析两个基于弯曲的移动传感节点（FMN）设计。新的设计克服了一些运动学上的局限性和在3D空间中FMN导航中经常遇到的实际实现问题，允许在3D空间中弯曲和扭曲顺从光束。两种FMN设计的离散线性CBM均已通过实验验证，并通过将计算结果与已发布数据进行了比较，并使用多重射击方法和有限元分析进行了仿真验证。

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