三支链六自由度并联骨外固定支架刚度优化设计  

Stiffness Optimal Design of a Three-Legged Six-DoF Parallel External Fixation Frame for Bone Fracture Reduction

作　　者：傅雨璇 霍欣明 齐杨 宋轶民[1,3] 孙涛 张弢[4] Fu Yuxuan;Huo Xinming;Qi Yang;Song Yimin;Sun Tao;Zhang Tao(School of Mechanical Engineering,Tianjin University,Tianjin 300350,China;School of Mechanical Engineering,Tianjin University of Technology and Education,Tianjin 300222,China;School of Mechanical Engineering,Ren’ai University of Tianjin,Tianjin 301636,China;Tianjin Hospital,Tianjin 300211,China)

机构地区：[1]天津大学机械工程学院,天津300350 [2]天津职业技术师范大学机械工程学院,天津300222 [3]天津仁爱学院机械工程系,天津301636 [4]天津市天津医院,天津300211

出　　处：《天津大学学报（自然科学与工程技术版）》2023年第4期361-371,共11页Journal of Tianjin University：Science and Technology

基　　金：国家重点研发计划资助项目(2018YFB130096);国家自然科学基金资助项目(62027812,51875391,51875392,51905378);天津市科技计划资助项目(20201193,18PTLCSY00080);天津市自然科学基金资助项目(20JCQNJC00360);天津市技术创新引导专项基金企业科技特派员项目(20YDTPJC00450);天津市高等学校科技发展基金计划资助项目(2020KJ105);天津职业技术师范大学科研启动项目(KYQD1901).

摘　　要：传统的下肢骨折治疗方案普遍存在复位精度差、易造成二次创伤与并发症、延迟愈合等局限性.随着现代医学和机器人学的交叉融合,基于六自由度并联机构的微创骨折复位与固定技术得到广泛关注和应用.现有六支链并联骨折外固定支架普遍存在术前CT扫描易造成伪影、影响骨折复位轨迹规划的不足.针对上述问题,本文设计了一种三支链六自由度并联外固定支架3-SPRP.由于此支架用于人体下肢骨折的复位与固定,为了满足外固定支架的轻质量高刚度需求,本文开展了将支架质量与刚度均视为优化目标的多目标优化设计.首先,采用闭环矢量法建立3-SPRP并联外固定支架的位置逆解模型,基于瞬时旋量建立运动/力映射模型;其次,采用半解析建模法建立3-SPRP并联外固定支架的静刚度模型,对比理论刚度模型与有限元仿真模型在6个典型位姿下的各向线刚度,验证支架刚度模型的准确性;最后,以瞬时变形能为刚度指标,将3-SPRP并联外固定支架的刚度与质量均视为优化目标,开展多目标优化计算,定义最小距离法确定支架刚度与质量的最佳匹配关系.优化后整机质量约为0.889 kg,相较于优化前仅增加24 g,而各向线/角刚度值普遍提升50%左右,表明3-SPRP并联外固定支架的刚度优化设计的有效性.上述工作将为后续三支链六自由度并联骨折外固定支架的物理样机制造与实验研究提供理论基础.Traditional therapies for lower-bone fractures generally have limitations such as poor repositioning accu-racy,secondary damage,and delayed recovery.With the cross-development of modern medicine and robotics,minimally invasive fracture reduction and fixation techniques based on 6 degree-of-freedom(DoF)parallel mecha-nisms have gained widespread attention and application.However,existing 6-legged parallel external fixation frames for bone fracture reduction suffer from artifacts on preoperative CT scans and interference during trajectory navigation.To address the above problems,a 3-legged 6-DoF parallel external fixation frame for bone fracture reduction is designed using the 3-SPRP parallel mechanism.Since this frame is used for reducing and fixing human lower-bone fractures,a multi-objective optimization that considers both the mass and the stiffness of the frame as optimization objectives is performed to meet the requirement of light mass and high stiffness of the external fixation frame.First,the inverse kinematics of the 3-SPRP parallel external fixation frame is implemented by the closed-loop vector method,and the motion/force mapping model is established based on the instantaneous rotational volume.Then,the static stiffness modeling of the 3-SPRP parallel external fixation frame is obtained through the virtual joint method,and its accuracy is verified by comparing the theoretical value of each linear stiffness with the finite-element simulation value at six measurement points.Finally,considering instantaneous deformation energy as the static stiffness index and both the stiffness and mass of the 3-SPRP parallel external fixation frame as optimization objectives,multiobjective optimization is performed,and the minimum distance method is defined to determine the best matching relationship between the stiffness and mass.The optimized mass is approximately 0.889 kg,only 24 g more than before optimization,and linear/angular stiffness values are generally improved by about 50%,proving the stiffness optimal design

关 键 词：并联骨折外固定支架 静刚度建模 多目标优化 

分 类 号：TK448.21[动力工程及工程热物理—动力机械及工程]