Full Cycle Solution for 3-D Offset Slider Crank Kinematics:Pseudographics - A Pedagogic Examination of a Non-TraditionalComputational Method

摘要

The slider crank is a mechanism that students encounter at an early stage in the study of both 2-D and 3-D kinematics. In the current paper this classic device is used as an exemplar for a coordinate geometry based method, with the coined name of “pseudographics”, that provides an option to the more familiar textbook vectorial approach. Pseudographics employs a commercial equation solving software to generate coordinates of the kinematic polygons for position, velocity and acceleration. The lines and arcs used to construct 2-D diagrams are replaced in 3-D pseudographics by equations for a straight line, a plane and the surface of a sphere. Because it avoids cross and dot products, matrices and repeated differentiations, the method has a lowered demand for skills in mathematics. The author sees pseudographics fulfilling the dual role of providing engineering students with an alternative to the prevalent textbook technique, and also opening a door to the understanding of mechanism kinematics to students who do not have a background in engineering mathematics. A determination of the angular velocity of the connecting rod is emphasized. Lecture experience has shown that the visualization of the motion of this member provides a learning challenge. Pseudographics uses 3-D coordinate geometry in conjunction with motion limitations for a single rigid body to identify kinematics features of the slider crank. Students appreciate that information on full cycle behaviour is necessary for design work, so output plots of some kinematic features for a revolution of the input driving crank are presented. Computer codes are appended. In closing, the paper summarizes the advantages and disadvantages of pseudographics in comparison to current textbook approaches to 3-D mechanisms. Student reaction is provided in brief, and future work in pseudographics is indicated.