Topology Optimization for Lightweight Design of Mechanical Legs of Hydraulic Bipedal Robots

doi:10.3969/j.issn.1004-132X.2026.09.011

Abstract

Abstract:

In lightweight design processes of bipedal robots， the optimization design of many parts had not yet achieved the ideal structural forms， and ultimately only rely on the designer’s experiences for subsequent adjustments and corrections. Thus， the existing topology optimization methods were systematically sorted out and introduced into the structural design of mechanical thighs. By constructing a mathematical model for lightweight optimization design of mechanical thighs， and following the topology optimization processes， the initial design geometric model of the mechanical thighs was designed with different unit densities and optimized minimum sizes. Finally， four topological structures were obtained， which reduce the mass by 535.4 g， 494.3 g， 423.8 g and 569.2 g respectively. According to the actual working conditions and machining process requirements， the third scheme was selected for strength simulation verification. The simulation results show that compared with the processed configuration， under the condition of set distributed force， the maximum displacement deformation of the optimized design is 0.9012 mm， which is significantly smaller than that of the original design of 1.188 mm； under the condition of set distributed force and torque resultant force， the maximum displacement deformation is 1.799 mm， which is also smaller than that of the original design of 2.377 mm. The component mass is reduced by 38.45%， and the performance of the optimized design is better than that of the original design， which verifies the accuracy of the finite element model and the effectiveness of the optimized design.

Key words: hydraulic bipedal robot, topology optimization, structural design, lightweight mechanical leg

摘要：

目前在双足机器人轻量化设计过程中，许多零件的优化设计仍未能获得理想的结构形态，最终只能依靠设计者的经验进行后续的调整和修正。基于此，对现有的拓扑优化方法进行了系统梳理，并将其引入机械大腿的结构设计中。通过构建机械大腿轻量化优化设计的数学模型，并按照拓扑优化的流程对机械大腿的初始设计几何模型进行了不同单元密度和优化最小尺寸的减重设计，最终获得了四种拓扑结构，分别使质量减小了535.4 g、494.3 g、423.8 g和569.2 g。根据实际工况和机加工工艺的要求，选择了第三种方案进行强度仿真校核，仿真结果表明，与已加工构型相比，在设定分布力的工况下，优化设计的最大位移变形量为0.9012 mm，明显小于原设计的最大位移变形量1.188 mm；在设定分布力及力矩合力的工况下，最大位移变形量为1.799 mm，也小于原设计的最大位移变形量2.377 mm。部件质量减小了38.45%，优化设计的性能表现优于原设计，验证了有限元模型的准确性及优化设计的有效性。

关键词: 液压双足机器人, 拓扑优化, 结构设计, 机械腿轻量化

CLC Number:

TH16

ZHU Jiayi, GAO Jie, GAO Liang, CAO Huai. Topology Optimization for Lightweight Design of Mechanical Legs of Hydraulic Bipedal Robots[J]. China Mechanical Engineering, 2026, 37(9): 2185-2193.

朱佳怡, 高杰, 高亮, 曹淮. 轻量化液压双足机器人机械腿拓扑优化设计[J]. 中国机械工程, 2026, 37(9): 2185-2193.

Figures/Tables 19

Fig.1 Hydraulic mechanical leg

Fig.2 Design of mechanical leg

Fig.3 Flow chart of robot leg topology optimization

Fig.4 Process of the processed design configuration

Fig.5 Initial configuration style

Fig.6 Analysis results of the initial configuration of the mechanical thigh

Fig.7 Topology optimization area settings

Fig.8 Topology optimization design results of scheme 1

Tab.1 Comparison of topology optimization results of robot legs in scheme 1

参数	初始结构	优化结构	优化比重/%
质量/g	1102.2	566.8	48.58
设定分布力的工况情况下位移变形量/mm	1.188	1.035	12.88
设定分布力及力矩合力的工况下位移变形量/mm	2.337	2.171	7.11

Fig.9 Topology optimization design results of scheme 2

Tab.2 Comparison of topology optimization results of robot legs in scheme 2

设定分布力及力矩合力的工况下位移变

形量/mm

2.337

2.034

12.97

Fig.10 Topology optimization design results of scheme 3

Tab.3 Comparison of topology optimization results of robot legs in scheme 3

参数	初始结构	优化结构	优化比重/%
质量/g	1102.2	678.4	38.45
设定分布力的工况下位移变形量/mm	1.188	0.9012	23.02
设定分布力及力矩合力的工况下位移变形量/mm	2.337	1.799	24.14

Fig.11 Topology optimization design results of scheme 4

Tab.4 Comparison of topology optimization results of robot legs in scheme 4

设定分布力及力矩合力的工况下位移变

形量/mm

2.337

2.206

5.61

Fig.12 Simulation analysis results

Fig.13 Design optimization displacement cloud diagram

Fig.14 Design optimization stress cloud diagram

Tab. 5 Comparison of the tenth-order frequency data between scheme 3 and the original design results

阶数	原始设计	方案三
一阶	3.103 10×10^-2	3.259 70×10^-2
二阶	0.169 14	0.191 54
三阶	0.242 25	0.284 98
四阶	0.266 28	0.300 92
五阶	0.450 64	0.527 40
六阶	0.710 55	0.756 10
七阶	0.864 98	0.958 02
八阶	1.2801	1.2923
九阶	1.3956	1.4811
十阶	1.5418	1.7636

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