Relationship between Stagger Angle Interval and Mechanism Type of the Bennett Mechanism

doi:10.3901/JME.2020.09.009

Abstract

Abstract: At present, Bennett (BNT) mechanism can be divided into two types according to the direction of axis of revolute joints:Asymmetrical and linear symmetrical installation. In order to study the similarities and differences between these two types of mechanisms, using adjacent quadrants were used to form four intervals in the region of link stagger angle (0, 2π). Then, a group of asymmetrically installed left-handed and right-handed BNT mechanisms are obtained based on the S₁₂(quadrant I and II) and S₃₄(quadrant III and IV)intervals, and a group of linearly symmetrically installed left-handed and right-handed BNT mechanisms are obtained based on the S₂₃(quadrant II and III)and S₄₁(quadrant IV and I)intervals. Comparing these two groups of mechanisms, only the axis is asymmetrical while the structure itself is symmetrical. Since the asymmetrical installation mechanisms in the regions of S₁₂ and S₃₄ can be transformed into linear symmetrical mechanisms in the region of S₄₁ by setting the stagger angle, there is no essential difference between linear symmetrical and asymmetrical mechanisms, and these two groups of mechanisms are essentially the same one. Because the joints within the mechanism in the region of S₄₁ have the same axial direction, and the positive direction of the axis is the same as the anti-clockwise angular displacement direction of the inner angle of the adjacent links, so the interval of R₄₁(quadrant IV and I)represented by the sharp angle of the stagger angle is used as the working interval of the stagger angle, then two basic types of BNT linear symmetrical mechanisms, i.e., right-handed and left-handed, are obtained. The kinematic chains of these two types of mechanisms are the same, but they are obtained by taking different components as the frame. According to these concepts, aiming to the left-handed and right-handed BNT mechanisms, the uniform structural parameter equations and the closed-loop displacement equations with the inner angles of adjacent links are given by using the stagger sharp angles. This unified parametric equation with sharp angles is simple, intuitive and easy to apply. A necessary constraint condition that the stagger angles of adjacent links cannot be selected in the same quadrant of the action region is emphasized and supplemented.

Key words: Bennett mechanism, constraint condition, stagger angle, structural parameters, closed-loop displacement equation

CLC Number:

TH112

LU Ling, ZHANG Yitong, MU Dejun, HU Bo, LU Wenjuan. Relationship between Stagger Angle Interval and Mechanism Type of the Bennett Mechanism[J]. Journal of Mechanical Engineering, 2020, 56(9): 9-17.

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