新型大行程柔顺并联机构理论与实验研究
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摘要
随着军事工程、光通信工程、生物工程、精密机械工程、精密光学工程等领域的科学技术不断发展，迫切需要各方面性能都更加出色的新型机构来适应越来越高的操作需求。合理构型的柔顺并联机构操作精度、响应速度、承载力、可控性、灵活性等方面都有比较出色的表现，但运动范围普遍较小，柔顺铰链的类型、材料的刚度和材料的弹性极限严格的限制了转动角度的大小。
本文对大行程柔顺虎克铰设计及大行程柔顺并联机构设计问题作了以下研究：
（1）设计了一种新型多簧片大变形柔顺虎克铰，通过伪刚体模型计算和非线性有限元仿真，验证了该铰链结构的合理性和模型的有效性，该设计基本符合虎克铰的转动特性。在虎克铰的初步设计基础上，又针对虎克铰的各项性能进行了多目标优化设计，增加运动行程、提高非功能方向的刚度、提高承载力、便于加工等，得到装配式柔顺虎克铰为最优结构。该柔顺虎克铰可实现高精度、大角度的二维转动运动，采用直线与曲线复合簧片对称分布柔度设计，提高了铰链的轴向刚度和径向刚度，当受到纯转矩作用时，基本没有轴心漂移，是一种性能优良的大行程柔顺虎克铰。
（2）基于大变形柔性虎克铰设计了PUU运动链，将4条PUU运动链对称布置，构造了一种空间三自由度大行程柔顺并联机构。使用螺旋理论对PUU运动链和并联机构的自由度进行了分析，建立了三自由度柔顺并联机构的等效伪刚体模型，推导了机构的位置反解方程和速度雅克比矩阵，并利用非线性有限元软件进行了模拟仿真，结果表明机构的等效伪刚体模型是有效的。这种三自由度柔顺并联机构可达立方厘米级的工作空间。
（3）基于大变形柔性虎克铰设计了PURU运动链和UC运动链，并使用4条PURU运动链和1条UC运动链，构造了一种空间四自由度大行程柔顺并联机构。使用螺旋理论对PURU运动链、UC运动链和并联机构的自由度进行了分析，建立了四自由度柔顺机构的等效伪刚体模型，推导了机构的位置反解和速度雅克比矩阵，根据柔性虎克铰的转角范围，分析了四自由度柔顺机构的工作空间。根据非线性有限元软件的比较结果，该柔顺机构可以输出高精度大位移的三维转动和一维平动。
(4)根据前述章节的分析结果，对大行程三自由度和四自由度柔顺并联机构的输出行程做了实验研究。根据实验结果，对相对误差进行了讨论，并根据误差来源对柔顺机构的等效伪刚体模型进行修正。使用修正公式进行的实验结果表明，修正公式是有效的，显著减小了相对误差。
With the constantly developing technology in the military engineering, opticalcommunication engineering, biological engineering, precision mechanical engineering andprecision optical engineering, there is an urgent need for the new-type robots, which possessmuch better performances in all aspects, that can adapt to the increasingly higherrequirements of operation. A well-designed compliant parallel mechanism has relatively goodperformances with respect to the operation accuracy, response speed, load-bearing capacity,controllability and flexibility. However, its rotational angle is so strictly limited by the type ofthe compliant hinge, material stiffness and the material elastic limit that the workspacegenerally tends to be small.
In this paper, we study the design of the large-deformation compliant hooke hinge andthe large-stroke compliant parallel mechanism. The study mainly consists of the followingthree parts:
(1) A new-type multi-reed hooke joints with large deformability is designed. Based onthe pseudo-rigid-body model and the nonlinear finite-element simulation results, we verify theeffectiveness of the hinge structure and the validity of the hinge model. This design accordwith the rotation characteristics of the hooke hinge. On the basis of the preliminary design ofthe hooke hinge, the multi-objective optimization designwith respect to all the hinge'sperformance indexes is implemented. The optimization is aimed at increasing the strokedistanceand the stiffness of the hinge at the non-functional direction, improving theload-bearing capacity, and reducing the manufacturing difficulty etc.. The optimizationproduces an ultimate structure called the assembled Compliant Hooke Joint that can achievehigh-precision, wide-angle, two-dimension rotational motion. The symmetric layout of thecomposite straight-curving flexible reeds improves both the axial and radial stiffness of thehinge. When only the torque is applied, there is no substantial axial drift. Therefore, theCompliant Hooke Joint is an excellent compliant hooke joint with large deformability.
(2) Based on the large-deformation compliant hooke joint, a PUU kinematic chain isdesigned. Arranging four PUU kinematic chain symmetrically, we build a large-stroke3-DOFs spatial compliant parallel mechanism. The freedom of motion of the PUU kinematicchains and the parallel mechanism are analyzed by using the spiral theory. And the equivalentpseudo-rigid-body model of the3-DOFs compliant parallel mechanism is established. Therobot’s inverse solution of the position and the Jacobi matrix of the speed are derived. Results from the non-linear finite-element simulation show that the equivalent pseudo-rigid bodymodel of the robot is effective. According to angle range of the compliant hooke hinge, the3-DOFs compliant parallel mechanism can reach a workspace of cubic centimeters.
(3) Based on the large-deformation compliant hooke joint, a PURU and a UC kinematicchain are designed. Arranging four PUU kinematic chains and one UC kinematic chain, webuild a large-stroke4-DOFs spatial compliant parallel mechanism. The DOFs of the PUUkinematic chains, the UC kinematic chain and the parallel mechanism are analyzed by usingthe spiral theory. And the equivalent pseudo-rigid-body model of4-DOFs compliant parallelmechanism is established. The robot’s inverse solution of the position and the Jacobi matrix ofthe speed are derived. With respect to angle range of the compliant hooke hinge, theworkspace of the4-DOFs compliant parallel mechanism is analyzed. According to thecomparison results of the nonlinear finite-element, this compliant robot can produce ahigh-precision large output of three-dimension rotation and one-dimension translation.
(4) Based on the above-mentioned studies, we conducted the experiments of3-DOFs and4-DOFs large-stroke compliant parallel mechanisms. Afterwards, the experiment errors werediscussed. And we then corrected the equivalent pseudo-rigid body model of the compliantparallel mechanisms according to the source of the errors. The experiment results of themodified formula shows that the modified formula is valid and can significantly reduce theexperiment errors.
本文对大行程柔顺虎克铰设计及大行程柔顺并联机构设计问题作了以下研究：
（1）设计了一种新型多簧片大变形柔顺虎克铰，通过伪刚体模型计算和非线性有限元仿真，验证了该铰链结构的合理性和模型的有效性，该设计基本符合虎克铰的转动特性。在虎克铰的初步设计基础上，又针对虎克铰的各项性能进行了多目标优化设计，增加运动行程、提高非功能方向的刚度、提高承载力、便于加工等，得到装配式柔顺虎克铰为最优结构。该柔顺虎克铰可实现高精度、大角度的二维转动运动，采用直线与曲线复合簧片对称分布柔度设计，提高了铰链的轴向刚度和径向刚度，当受到纯转矩作用时，基本没有轴心漂移，是一种性能优良的大行程柔顺虎克铰。
（2）基于大变形柔性虎克铰设计了PUU运动链，将4条PUU运动链对称布置，构造了一种空间三自由度大行程柔顺并联机构。使用螺旋理论对PUU运动链和并联机构的自由度进行了分析，建立了三自由度柔顺并联机构的等效伪刚体模型，推导了机构的位置反解方程和速度雅克比矩阵，并利用非线性有限元软件进行了模拟仿真，结果表明机构的等效伪刚体模型是有效的。这种三自由度柔顺并联机构可达立方厘米级的工作空间。
（3）基于大变形柔性虎克铰设计了PURU运动链和UC运动链，并使用4条PURU运动链和1条UC运动链，构造了一种空间四自由度大行程柔顺并联机构。使用螺旋理论对PURU运动链、UC运动链和并联机构的自由度进行了分析，建立了四自由度柔顺机构的等效伪刚体模型，推导了机构的位置反解和速度雅克比矩阵，根据柔性虎克铰的转角范围，分析了四自由度柔顺机构的工作空间。根据非线性有限元软件的比较结果，该柔顺机构可以输出高精度大位移的三维转动和一维平动。
(4)根据前述章节的分析结果，对大行程三自由度和四自由度柔顺并联机构的输出行程做了实验研究。根据实验结果，对相对误差进行了讨论，并根据误差来源对柔顺机构的等效伪刚体模型进行修正。使用修正公式进行的实验结果表明，修正公式是有效的，显著减小了相对误差。
With the constantly developing technology in the military engineering, opticalcommunication engineering, biological engineering, precision mechanical engineering andprecision optical engineering, there is an urgent need for the new-type robots, which possessmuch better performances in all aspects, that can adapt to the increasingly higherrequirements of operation. A well-designed compliant parallel mechanism has relatively goodperformances with respect to the operation accuracy, response speed, load-bearing capacity,controllability and flexibility. However, its rotational angle is so strictly limited by the type ofthe compliant hinge, material stiffness and the material elastic limit that the workspacegenerally tends to be small.
In this paper, we study the design of the large-deformation compliant hooke hinge andthe large-stroke compliant parallel mechanism. The study mainly consists of the followingthree parts:
(1) A new-type multi-reed hooke joints with large deformability is designed. Based onthe pseudo-rigid-body model and the nonlinear finite-element simulation results, we verify theeffectiveness of the hinge structure and the validity of the hinge model. This design accordwith the rotation characteristics of the hooke hinge. On the basis of the preliminary design ofthe hooke hinge, the multi-objective optimization designwith respect to all the hinge'sperformance indexes is implemented. The optimization is aimed at increasing the strokedistanceand the stiffness of the hinge at the non-functional direction, improving theload-bearing capacity, and reducing the manufacturing difficulty etc.. The optimizationproduces an ultimate structure called the assembled Compliant Hooke Joint that can achievehigh-precision, wide-angle, two-dimension rotational motion. The symmetric layout of thecomposite straight-curving flexible reeds improves both the axial and radial stiffness of thehinge. When only the torque is applied, there is no substantial axial drift. Therefore, theCompliant Hooke Joint is an excellent compliant hooke joint with large deformability.
(2) Based on the large-deformation compliant hooke joint, a PUU kinematic chain isdesigned. Arranging four PUU kinematic chain symmetrically, we build a large-stroke3-DOFs spatial compliant parallel mechanism. The freedom of motion of the PUU kinematicchains and the parallel mechanism are analyzed by using the spiral theory. And the equivalentpseudo-rigid-body model of the3-DOFs compliant parallel mechanism is established. Therobot’s inverse solution of the position and the Jacobi matrix of the speed are derived. Results from the non-linear finite-element simulation show that the equivalent pseudo-rigid bodymodel of the robot is effective. According to angle range of the compliant hooke hinge, the3-DOFs compliant parallel mechanism can reach a workspace of cubic centimeters.
(3) Based on the large-deformation compliant hooke joint, a PURU and a UC kinematicchain are designed. Arranging four PUU kinematic chains and one UC kinematic chain, webuild a large-stroke4-DOFs spatial compliant parallel mechanism. The DOFs of the PUUkinematic chains, the UC kinematic chain and the parallel mechanism are analyzed by usingthe spiral theory. And the equivalent pseudo-rigid-body model of4-DOFs compliant parallelmechanism is established. The robot’s inverse solution of the position and the Jacobi matrix ofthe speed are derived. With respect to angle range of the compliant hooke hinge, theworkspace of the4-DOFs compliant parallel mechanism is analyzed. According to thecomparison results of the nonlinear finite-element, this compliant robot can produce ahigh-precision large output of three-dimension rotation and one-dimension translation.
(4) Based on the above-mentioned studies, we conducted the experiments of3-DOFs and4-DOFs large-stroke compliant parallel mechanisms. Afterwards, the experiment errors werediscussed. And we then corrected the equivalent pseudo-rigid body model of the compliantparallel mechanisms according to the source of the errors. The experiment results of themodified formula shows that the modified formula is valid and can significantly reduce theexperiment errors.
引文
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