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摘要:
带移动副平面六连杆机构的分支、运动缺陷、运动范围等的判别是机构运动特性研究的重要指标。首先，将带2个移动副或3个移动副的平面六连杆机构分为四环链及五环链，引入欧拉公式、三角换元等方法，得到带移动副机构在极限位置（包括死点、分支点）的具体构型、具体关节输入输出关系以及关节旋转空间。其次，将2个链路结合，提出带2个移动副及3个移动副平面六连杆机构的分支识别方法。最后，通过实例验证，得到机构的分支点、死点及关节在所有极限位置的具体角度，为带移动副机构分支的自动识别提供了一种简便有效的方法。
Abstract:The identification of branch, motion defect and range of motion of the planar six-bar linkages with sliding pairs is an important indicator for motion characteristics of linkages. Firstly, this paper divides the planar six-bar linkages with two sliding pairs or three sliding pairs into four-bar chain or five-bar chain. B-ring in Euler's formula and trigonometric substitution method, the specific configurations (including branch points and dead points) of the planar linkages with sliding pairs in their limit positions, input and output relationship and joint rotation space are obtained. Secondly, this paper combines two chains and proposes a method for the branch identification of planar six-bar linkages with two or three sliding pairs. Finally, this paper verifies the proposed method with examples of planar six-bar linkages with two and three sliding pairs. The branches, dead points and the specific angles of joints in limit positions of the two mechanisms are calculated. The proposed method gives a convenient and effective way for the automatic branch identification of planar linkages with sliding pairs.
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Key words:
- sliding pairs /
- planar six-bar linkages /
- limit position /
- branch /
- joint rotation space
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图 5 带2个移动副平面六连杆机构分支识别流程
Figure 5. Flowchart of branch identification of planar six-bar linkage with two sliding pairs
图 6 带2个移动副平面六连杆机构分支曲线
Figure 6. Curve of branches of planar six-bar linkage with two sliding pairs
图 7 带2个移动副平面六连杆机构实例的分支曲线
Figure 7. Curve of branches of planar six-bar linkage with two sliding pairs
图 8 带2个移动副平面六连杆机构Δ4随θ2变化曲线
Figure 8. Change of Δ4 with θ2 for planar six-bar linkage with two sliding pairs
表 1 带2个移动副平面六连杆机构参数
Table 1. Parameters of planar six-bar linkage with two sliding pairs
参数 数值 a1 2.4 a2 5.5 a3 4.8 a4 4.2 a5 2.5 a7 2.4 β/(°) 45 α1/(°) 30 α2/(°) 50 
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表 2 带2个移动副平面六连杆机构的分支点
Table 2. Branch points of planar six-bar linkage with two sliding pairs
分支点 θ2/(°) θ3/(°) θ4/(°) θ5/(°) 1 -161.4 -28.6 16.4 120 2 -141.6 -92.2 -47.2 -60 3 -105.5 55.3 100.3 120 4 -15.6 91.3 136.3 120 5 7.9 -152.7 -107.7 -60 6 72.6 -74.6 -29.6 120
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表 3 带2个移动副平面六连杆机构的死点
Table 3. Dead points of planar six-bar linkage with two sliding pairs
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表 4 带3个移动副平面六连杆机构参数
Table 4. Parameters of planar six-bar linkage with three sliding pairs
参数 数值 a1 3 a2 6 a3 5.2 a4 5 a7 4 β/(°) 50 γ/(°) 30 α1，α2/(°) 30
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表 5 带3个移动副平面六连杆机构的死点
Table 5. Dead points of planar six-bar linkage with three sliding pairs
死点 θ2/(°) θ3/(°) θ4/(°) a -78.9 -40.0 10.0 b -158.9 -40.0 10.0
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表 6 带2个移动副平面六连杆机构的2个位置参数
Table 6. Parameters of planar six-bar linkage with two sliding pairs for 2 positions
参数 位置1 位置2 θ2/(°) -50 10 B (3.54, -4.21) (5.42, 0.96) E (2.94, -0.06) (1.75, -1.10) F (1.32, 1.85) (-0.12, -2.97) Δ4 0.25 -0.34
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