Application of homogenous transformation matrix to the design and machining of a Geneva mechanism with curved slots

Abstract

The current paper presents a simple yet comprehensive method for the design and machining of a Geneva indexing mechanism with curved slots. In the proposed approach, a kinematic model of the Geneva mechanism is developed using homogenous coordinate transformation and conjugate surface theory. The pressure angle of Geneva mechanism and the principal curvatures of the curved slots are analysed using an analytical expression derived for the slot profile. The NC data required to machine the driven with curved slots are derived from the CNC link variables by equating the machine tool ability function and the tool location matrix. The proposed design methodology is verified by machining the designed curved slots using a three-axis CNC machine. The results confirm that the approach presented in this study enables the Geneva mechanism design and manufacturing tasks to be successfully integrated, thus making possible a flexible, automatic, cost efficient, and controllable production process.