Abstract:

This paper presents a simplified approach that we have adopted for teaching to BSc students of Mechanical Engineering at the University of Bergamo a rather complex subject, as the kinematic synthesis of planar mechanisms.

Since a lot of years mechanisms are taught in the "general" course of “Mechanical Systems Engineering”, during fifth semester, focusing mainly on kinematic analysis methods, spanning from graphical methods to complex number representation and to simulation using multibody commercial codes. Detailed methods for mechanisms synthesis and optimization are given only to MSc students of the Mechatronics and Design curricula.

To give BSc students the feeling of linkages synthesis, a geometric constraint programming approach is used ([1] Waldron et al.), based on the sketching mode of a commercial parametric computer-aided-design software, which is used in our course of “Technical Drawings for Industry” (first semester).

Linkages are typically used to transform the input motion from a mover into the desired output motion of the follower, or to constrain a rigid body to follow a specific path. The “functional synthesis” of a linkage often presents many difficulties, for the lack of generalized design criteria, and usually requires experience and ingenuity that BCs students cannot still have. Traditionally, there are 3 approaches to solve this problem: “trial-and-error” method, analytical techniques and graphical methods. From an educational point of view each of them has pros and cons. The most demanding approach is the “trial-and-error” method, wherein iterated analysis of the current solution are carried out and the designer have to adjust the mechanism parameters to get a reasonable solution that satisfies the prescribed performance; this approach requires an high mechanical intuition in order to properly modify the mechanism parameters. In analytical techniques the prescribed constraints are formulated and the synthesis is performed in a pure numerical fashion, but although this approach can cope with complex problems it is not useful to develop the students’ mechanical intuition. Finally the graphical synthesis uses rather simple graphical procedures to determine the linkage parameters but this method can be time consuming and tedious for the designer.

The advantage of the proposed approach is that the formulation of the problem is very intuitive, doesn’t require an advanced background in kinematics and no complex details on numerical analysis are needed. More in detail, using the CAD sketching mode, the prescribed geometrical constraints are imposed graphically through the relationship toolbar; afterwards the software ‘s numerical solver gives feasible solutions whose quality can be immediately checked, helping students to develop geometric insight and mechanical sensibility.

Moreover the geometric constraint programming technique is also profitably used for determining the workspace boundaries of serial and parallel manipulators in the course on “Mechanics of Robots” (first semester of MSc Mechanical Engineering).

References:
[1] K.J. Waldron, G.L. Kinzel, S.K. Agrawal (2016) “Kinematics, Dynamics, and Design of Machinery, 3rd Edition”, Wiley

Keywords:

Linkage synthesis, computer-aided design, workspace.