Design of a tumbling machine (mixer) using a statically determinate spatial mechanism and determination of rational geometric parameters

The object of this study is tumbling equipment in which working containers execute a complex spatial motion. Articulated spatial mechanisms are widely used in various branches of industry, particularly in mechanical engineering, including mechanisms that contain passive constraints in their structure. The presence of passive constraints can cause operational problems and negatively affect equipment reliability. Therefore, an important task is the synthesis of articulated spatial mechanisms through modification of existing structures in order to eliminate passive constraints. This paper reports the synthesis of a statically determined seven-link articulated spatial mechanism with revolute kinematic pairs. A technique for eliminating a passive constraint in the structure of an articulated spatial mechanism has been proposed, which allows for its static determinacy. As a result, the need to compensate for inaccuracies in geometric relationships between the links by means of clearances in the kinematic pairs is eliminated, making it possible to improve operational characteristics and prolong service life. The introduction of an auxiliary link into the spatial kinematic chain creates conditions for effective implementation of tumbling technological operations by increasing the amplitude of spatial displacement of the container. Analytical relationships between the main geometric parameters of the seven-link spatial mechanism that determine its operability have been established. The derived mathematical dependences allow a justified selection of rational geometric parameters at the design stage and provide a basis for calculating key geometric characteristics for further engineering application in industrial practice.