3-PRPS/RRR踝关节康复机器人运动机理研究与试验

doi:10.12382/bgxb.2022.0430

摘要/Abstract

摘要：

为设计一种结构合理、适宜患者使用的踝关节康复机构,针对踝关节运动特点,提出一种3-PRPS/RRR并联机器人。采用旋量理论描述机器人的数学模型,推导得出该机器人具有3转动自由度;使用闭环矢量法得到机器人的位置逆解方程,利用粒子群优化算法计算机器人的位置正解;设定一组机器人的设计参数,建立由初值不断迭代的数值算法得到机器人的工作空间;推导机器人的雅克比矩阵,计算机器人在其工作空间内的奇异位形;通过生物力学软件建立人体骨肌系统,仿真得到使用该机器人进行踝关节康复训练时踝关节处肌肉的激活程度;搭建试验样机进行试验,验证机器人位置正/逆解、工作空间和奇异位形。研究结果表明:CAD模型和理论计算结果一致,结合试验验证了机器人位置正/逆解的正确性;试验样机的工作空间能够满足踝关节康复训练所需的运动范围,且机器人在其工作空间内不存在奇异位形;使用该机器人进行康复训练时能够有效地激活肌肉,达到康复训练的目的。

关键词: 康复机器人, 踝关节, 位置正逆解, 工作空间, 奇异位形, 骨肌系统

Abstract:

To design a rational and patient-suited ankle joint rehabilitation mechanism, a novel 3-PRPS/RRR parallel robot is proposed, tailored to the specific characteristics of ankle joint movement. The mathematical model of the mechanism is described using the screw theory, demonstrating its three degrees of freedom. The closed-loop vector method is used to obtain the inverse kinematics of the mechanism, and the particle swarm optimization is used to calculate the forward kinematics. Design parameters are meticulously set, and the workspace of the mechanism is determined by the iterative numerical algorithm based on the initial value. The biomechanical software is used to establish the human musculoskeletal system, and the activation of muscles is simulated when the mechanism is used for ankle rehabilitation training. Finally, an experimental prototype is built to verify the forward and inverse kinematics, workspace and singular configuration of the mechanism. The results show that the CAD model is consistent with the theoretical calculations, thereby validating the accuracy of the forward and inverse kinematics of the mechanism through experiments. The working space of experimental prototype can meet the range of motion required by ankle rehabilitation training, and there is no singular configuration in the working space of the mechanism. This mechanism can effectively activate muscles and achieve the purpose of rehabilitation training.

Key words: rehabilitation robot, ankle joint, forward and inverse kinematics, workspace, singular configuration, musculoskeletal system

中图分类号:

TH112.1

李辉, 宁峰平, 郭辉, 李瑞琴. 3-PRPS/RRR踝关节康复机器人运动机理研究与试验[J]. 兵工学报, 2023, 44(10): 3026-3037.

LI Hui, NING Fengping, GUO Hui, LI Ruiqin. Research and Experiment on the Motion Mechanism of a 3-PRPS/RRR Ankle Rehabilitation Mechanism[J]. Acta Armamentarii, 2023, 44(10): 3026-3037.

图/表 29

图1 踝关节康复机器人模型

Fig.1 Ankle rehabilitation robot model

图2 PSO算法流程图

Fig.2 Flow chart of the PSO algorithm

表1 机构的设计参数

Table 1 Design parameters of the mechanism

参数	数值	参数	数值
l₁₁/mm	160	l₂₃/mm	60
l₁₂/mm	147.5	l₄/mm	265
l₁₃/mm	147.5	p₁/mm	156.4641
l₂₁/mm	60	p₂/mm	154.7974
l₂₂/mm	60	p₃/mm	154.7974

表2 Di在动坐标系中的初始坐标

Table 2 Initial coordinates of Di in the moving coordinate system

参数	数值
D₁₀/mm	[55 0 -89]^T
D₂₀/mm	[-30 45 -89]^T
D₃₀/mm	[-30 -45 -89]^T

表3 PSO算法参数

Table 3 PSO algorithm parameters

参数	数值	参数	数值
c₁	1.49445	ω_min	0.2
c₂	1.49445	t_max	200
ω_max	0.8

表4 位置正解算例

Table 4 Examples of forward kinematic solutions

算例	q₁/mm	q₂/mm	q₃/mm	卦限	x/mm	y/mm	z/mm	α/(°)	β/(°)	γ/(°)	F
1	157.4	166.5	168.9	2	75.97	0.68	193.07	-3.44	0.09	8.67	1.87×10^-4
				3	53.96	12.59	176.25	-13.60	-13.26	12.72	1.07×10^-11
2	166.5	149.5	164.8	4	75.42	38.12	203.32	14.78	-20.72	15.72	2×10^-6
				8	86.73	9.84	209.42	16.07	-24.12	-2.44	0
3	168.9	174.3	160.9	2	27.8	-13.52	165.05	-10.26	-17.26	4.92	1.42×10^-14
				3	55.66	51.38	192.83	10.89	-13.48	55.53	1.11×10^-11

图3 适应度曲线

Fig.3 Fitness curves

图4 算例1的位姿

Fig.4 Poses of example 1

图5 算例2的位姿

Fig.5 Poses of example 2

图6 算例3的位姿

Fig.6 Poses of example 3

图7 机构的工作空间

Fig.7 Workspace of the mechanism

图8 D1的工作空间

Fig.8 Workspace of D1

图9 坐姿下踝关节康复机器人-人体骨肌耦合系统

Fig.9 Ankle rehabilitation robot-human musculoskeletal coupling system under sitting posture

图10 跖屈/背屈运动

Fig.10 Plantarflexion/dorsiflexion motion 】

图11 内翻/外翻运动

Fig.11 Inversion/eversion motion

图12 内收/外展运动

Fig.12 Adduction/abduction motion

图13 跖屈/背屈时肌肉激活度

Fig.13 Muscle activation during plantarflexion/dorsiflexion motion

图14 内翻/外翻时肌肉激活度

Fig.14 Muscle activation during inversion/eversion motion

图15 内收/外展时肌肉激活度

Fig.15 Muscle activation during adduction/abduction motion

图16 试验样机

Fig.16 The experimental prototype

表5 试验样机的设计参数

Table 5 Design parameters of the experimental prototype

参数	数值	参数	数值
l₁₁/mm	197	l₂₃/mm	43
l₁₂/mm	152.5	l₄/mm	293
l₁₃/mm	152.5	p₁/mm	195
l₂₁/mm	43	p₂/mm	174
l₂₂/mm	43	p₃/mm	174

图17 算例1的验证

Fig.17 Verification of example 1

图18 算例2的验证

Fig.18 Verification of example 2

图19 算例3的验证

Fig.19 Verification of example 3

表6 位置正解验证

Table 6 Verification of forward kinematic solutions mm

算例	卦限	理论输入值			实测输入值
算例	卦限	q₁	q₂	q₃	q₁	q₂	q₃
1	2	157.40	164.80	149.30	156.04	163.46	150.74
	3	157.40	164.80	149.30	155.88	163.65	148.98
2	4	166.50	149.50	164.80	168.01	151.12	164.77
	8	157.40	164.80	149.30	164.69	148.93	164.82
3	2	168.90	174.30	160.90	170.19	175.34	159.51

图20 两个指定位姿

Fig.20 Two specified poses

图21 工作空间试验

Fig.21 Workspace experiment

图22 电动推杆伸缩量变化

Fig.22 Variation of the stroke of the linear actuator

图23 动平台角度变化

Fig.23 Variation of the angle of the moving platform

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