复杂多环路连杆机构曲柄判定的分支图识别法

聂良益; 丁华锋; 王君; 毕树生

doi:10.13700/j.bh.1001-5965.2021.0152

复杂多环路连杆机构曲柄判定的分支图识别法

doi: 10.13700/j.bh.1001-5965.2021.0152

聂良益^{1, 2},
丁华锋^2, ,,
王君³,
毕树生⁴

1.
湖北理工学院机电工程学院, 黄石 435003
2.
中国地质大学(武汉) 机械与电子信息学院, 武汉 430074
3.
湖北工业大学机械工程学院, 武汉 430068
4.
北京航空航天大学机械工程及自动化学院, 北京 100083

基金项目:

国家自然科学基金 51975544

湖北省自然科学基金 2019AAA071

湖北理工学院人才引进项目 420202100760

详细信息

通讯作者:
丁华锋, E-mail: dhf@ysu.edu.cn

中图分类号: TH112.1
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- 文章访问数: 382
- HTML全文浏览量: 109
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- 被引次数: 0
出版历程
- 收稿日期: 2021-03-29
- 录用日期: 2021-07-10
- 网络出版日期: 2021-08-17
- 整期出版日期: 2022-10-20

Branch graph method for crank judgement of complex multi-loop linkage

NIE Liangyi^{1, 2},
DING Huafeng^{2
, ,},
WANG Jun³,
BI Shusheng⁴

1.
School of Mechanical and Electrical Engineering, Hubei Polytechnic University, Huangshi 435003, China
2.
School of Mechanical Engineering and Electronic Information, China University of Geosciences (Wuhan), Wuhan 430074, China
3.
School of Mechanical Engineering, Hubei University of Technology, Wuhan 430068, China
4.
School of Mechanical Engineering and Automation, Beihang University, Beijing 100083, China

Funds:

National Natural Science Foundation of China 51975544

Hubei Provincial Natural Science Foundation of China 2019AAA071

Talent Introduction Project of Hubei Polytechnic University 420202100760

More Information

Corresponding author: DING Huafeng, E-mail: dhf@ysu.edu.cn

摘要

摘要:
曲柄是连杆机构运动学分析的一个重要环节，其决定着机构的运动状态。现有的Grashof定理、N杆旋转定理可以很好地解决只含有转动副单闭环连杆机构的曲柄判定问题，但对于广泛应用于航空航天的复杂多环路连杆机构的曲柄判定，至今没有通用有效的解决手段。基于此，提出了复杂多环路连杆机构曲柄判定的分支图识别法。通过复杂多环路连杆机构内各个环路的杆件关系不等式，确定了其曲柄存在的第一个充分条件；结合连杆机构的运动分支识别图活动关节旋转范围确定了曲柄存在的第二个充分条件。在归纳了曲柄存在充分条件基础上，利用所提方法在平面4R、5R连杆机构做了实例分析，并与现有公认结果进行对比，验证了方法的有效性。在仅含转动副复杂多环路Stephenson六杆机构上进行了曲柄判定，证明了方法的可行性。
- 曲柄判定 /
- 分支识别 /
- Grashof定理 /
- N杆旋转定理 /
- 多环路连杆机构
Abstract:
Crank judgement is an important link in kinematic analysis of mechanisms, which determines the motion state of the mechanism. The existing Grashof theorem and N-bar rotation theorem can well solve the problem of crank judgement of single closed-loop linkage with only R joints, but there is no general and effective solution for crank judgement of complex multi-loop linkage widely used in aerospace. A branch graph identification method for determining the crank of complex multi-loop linkage is proposed. This method first determines the first sufficient condition for the existence of the crank through the inequality of the link relationship of each loop in the complex multi-loop linkage, and then determines the second sufficient condition for the existence of the crank by combining the branch graph of the linkage with the rotation range of the movable joint. On the basis of summing up the sufficient conditions, this method is used to analyze the planar 4R and 5R linkages, and the outcomes are compared with the existing recognized results, verifing the effectiveness of this method. Finally, the crank judgment is carried out on a complex multi-loop Stephenson six-bar linkage with only rotating pairs, which proves the feasibility of the method.
- crank judgement /
- branch identification /
- Grashof theorem /
- N-bar rotation theorem /
- multi-loop linkage

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图 1 平面4R连杆机构

Figure 1. Planar four-bar linkage

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图 2 平面4R连杆机构曲柄存在情况

Figure 2. Cranks of planar four-bar linkages

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图 3 平面5R连杆机构

Figure 3. Planar five-bar linkage

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图 4 平面5R连杆机构曲柄判定流程

Figure 4. Flowchart of crank judgement of planar five-bar linkage

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图 5 平面5R连杆机构的曲柄

Figure 5. Cranks of planar five-bar linkages

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图 6 平面4R连杆机构曲柄分支识别图

Figure 6. Crank judgement of planar four-bar linkage with branch graph

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图 7 平面5R连杆机构曲柄分支识别图(对应图 5(a)平面5R连杆机构)

Figure 7. Crank judgement of planar five-bar linkage with branch graph (Fig. 5(a))

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图 8 平面5R连杆机构曲柄分支识别图(对应图 5(b)平面5R连杆机构)

Figure 8. Crank judgement of planar five-bar linkage with branch graph (Fig. 5(b))

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图 9 平面5R连杆机构曲柄分支识别图(对应图 5(c)平面5R连杆机构)

Figure 9. Crank judgement of planar five-bar linkage with branch graph (Fig. 5(c))

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图 10 平面5R连杆机构曲柄分支识别图(对应图 5(d)平面5R连杆机构)

Figure 10. Crank judgement of planar five-bar linkage with branch graph (Fig. 5(d))

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图 11 Stephenson六杆机构

Figure 11. Stephenson six-bar linkage

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图 12 Stephenson六杆机构曲柄分支识别图(四链环路输入)

Figure 12. Branch graph for crank judgement of Stephenson six-bar linkage (input joint in four-bar loop)

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图 13 Stephenson六杆机构输入θ₂曲柄分支识别图(四链环路输入)

Figure 13. Crank judgement of Stephenson six-bar linkage using branch graph with input angle θ₂

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图 14 Stephenson六杆机构分支识别图(五链环路输入)

Figure 14. Branch graph of Stephenson six-bar linkage with input angle in five-bar loop

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图 15 Stephenson六杆机构输入θ₆曲柄分支识别图(五链环路输入)

Figure 15. Crank judgement of Stephenson six-bar linkage using branch graph with input angle θ₆

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表 1 图 2(a)双摇杆机构杆长参数

Table 1. Parameters of double rocker linkage in Fig. 2(a)

杆号	杆1	杆2	杆3	杆4
杆长/dm	26.5	14.7	26.7	26

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表 2 图 2(b)曲柄摇杆机构杆长参数

Table 2. Parameters of crank-rocker linkage in Fig. 2(b)

杆号	杆1	杆2	杆3	杆4
杆长/cm	13.2	62.2	35.6	56.7

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表 3 图 2(c)双曲柄机构杆长参数

Table 3. Parameters of double crank linkage in Fig. 2(c)

杆号	杆1	杆2	杆3	杆4
杆长/cm	15.2	22.1	25.6	10.6

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表 4 图 5(a)平面5R连杆机构杆长参数

Table 4. Parameters of five-bar linkage in Fig. 5(a)

杆号	杆1	杆2	杆3	杆4	杆5
杆长/cm	8	10	19	21	24

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表 5 图 5(b)平面5R连杆机构杆长参数

Table 5. Parameters of five-bar linkage in Fig. 5(b)

杆号	杆1	杆2	杆3	杆4	杆5
杆长/cm	10	13	19	21	24

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表 6 图 5(c)平面5R连杆机构杆长参数

Table 6. Parameters of five-bar linkage in Fig. 5(c)

杆号	杆1	杆2	杆3	杆4	杆5
杆长/cm	12	14	16	20	45

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表 7 图 5(d)平面5R连杆机构杆长参数

Table 7. Parameters of five-bar linkage in Fig. 5(d)

杆号	杆1	杆2	杆3	杆4	杆5
杆长/cm	20	25	30	42	45

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表 8 图 12 Stephenson六杆机构杆长对应参数

Table 8. Parameters of Stephenson six-bar linkage in Fig. 12

参数	数值
a₁/dm	2.67
a₂/dm	3.6
a₃/dm	2.71
a₄/dm	1
a₅/dm	4.2
a₆/dm	5
a₇/dm	3.4
a₉/dm	4.2
α/(°)	25
β/(°)	5

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表 9 图 13 Stephenson六杆机构输入θ₂曲柄对应参数

Table 9. Parameters of Stephenson six-bar linkage with input joint θ₂ in Fig. 13

参数	数值
a₁/dm	1
a₂/dm	3.6
a₃/dm	2.71
a₄/dm	2.67
a₅/dm	5.6
a₆/dm	5.6
a₇/dm	5.7
a₉/dm	2
α/(°)	25
β/(°)	5

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表 10 图 14 Stephenson六杆机构杆长对应参数

Table 10. Parameters of Stephenson six-bar linkage in Fig. 10

参数	数值
a₂/dm	5.6
a₄/dm	1
a₅/dm	4.2
a₆/dm	5
a₇/dm	3.4
a₈/dm	2.67
a₉/dm	5.6
a₁₀/dm	2.2
η/(°)	5
λ/(°)	25

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表 11 图 15 Stephenson六杆输入θ₅曲柄对应参数

Table 11. Parameters of Stephenson six-bar linkage with input joint θ₅ in Fig. 11

参数	数值
a₂/dm	1
a₄/dm	1.5
a₅/dm	9
a₆/dm	1
a₇/dm	7.3
a₈/dm	3.9
a₉/dm	7.4
a₁₀/dm	8.9
η/(°)	5
λ/(°)	25

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