Abstract
Abstract. In this paper, we present a solution-region-based synthesis approach for selecting optimal four-bar linkages with a Ball–Burmester point. We discuss both general and special cases of the Burmester point that coincide with the Ball point at the pole of the inflection circle. Given the coordinates of one fixed joint, any point on the target's straight line, and the direction of this straight line, we can synthesize an infinite number of mechanisms using a coupler curve with five-point contacts with its tangent by adopting the proposed approach. Each initial parameter corresponds to three side links that can generate three four-bar mechanisms. We generate different mechanism property charts by developing mechanism software that enables users to intuitively identify relevant linkage information and select the optimal linkage. This novel approach is a visualized analytical method for synthesizing and selecting optimal four-bar linkages with one Ball–Burmester point on its coupler curve.
Highlights
Tesar et al (1967) and Vidosic and Tesar (1967a, b) derived a series of synthesis formulas, and transformed the results into design diagrams for users according to three different cases, i.e., the general case of the Ball–Burmester point, the special case of the Ball– Burmester point at the inflection pole, and the special case of the Ball-Double Burmester point
We present a visualized synthesis approach based on the solution region for selecting optimal four-bar linkages with a Ball–Burmester point
We discuss both the general and special cases of the Burmester point that coincide with the Ball point at the pole of the inflection circle
Summary
As an important planar four-bar mechanism, four-bar linkages that approximate a straight line have been widely studied based on the theory of the kinematic geometry of mechanisms (Dijksman, 1976; Hunt, 1987; McCarthy, 2000; Wang and Wang, 2015). Dijksman (1972) and Dijksman and Smails (2000) used a geometrical method to discuss the Ball point in different configurations. Tesar et al (1967) and Vidosic and Tesar (1967a, b) derived a series of synthesis formulas, and transformed the results into design diagrams for users according to three different cases, i.e., the general case of the Ball–Burmester point, the special case of the Ball– Burmester point at the inflection pole, and the special case of the Ball-Double Burmester point. Yu et al (2013) presented a numerical comparison synthesis method for single and double straight-line guidance mechanisms to solve fourbar straight-line guidance mechanism synthesis problems for an arbitrarily given straight line’s “angle requirement” and “point-position requirement”. Han (1993) studied the synthesis of the four-bar straight-line linkage of Ball and Burmester points in general cases. Han (1993) studied the synthesis of the four-bar straight-line linkage of Ball and Burmester points in general cases. The author Yin et al (2011, 2012) studied the synthesis of the straight-line linkage of Ball and Burmester points, separately. We present a visualized synthesis approach based on the solution region for selecting optimal four-bar linkages with a Ball–Burmester point. We discuss both the general and special cases of the Burmester point that coincide with the Ball point at the pole of the inflection circle. Different mechanism property charts are generated by developing mechanism software to enable users to intuitively identify information about the involved linkages and to select the optimal linkage from an infinite number of mechanism solutions
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