Reciprocal Frame (RF) is a three-dimensional grillage structure that consists of mutually supported elements. In RF, whatever the composition that is built, the geometry should always have two members that are connected at a time. Moreover, at least three members should be connected to create a grid, but there is no limit for the maximum. In the research that has been done until today, the geometry of RF, form-finding issues, connections, structural behavior, fabrication methods were studied, but there is very limited number of studies about kinetic RF. In this study RF structures for single loop 3-, 4-, and 5-nexor configurations are analyzed in terms of their motion capabilities. The kinematic diagrams are drawn and their mobilities are calculated. Zero, single, and multi Degrees of Freedom (DoF) configurations are obtained. It has been found that the configurations with revolute joint series get minimum value and also it is not necessary to use as many joints as possible or joints with as many DoF as possible in the configuration to get maximum mobility value.

This study aims to develop missing geometric knowledge for demountable reciprocal frames (RF). While designing a demountable RF, one should know the initial, in-process and final form of the RF. These processes require some specific geometric knowledge. There are some deficiencies about geometric properties in the previous studies about demountable RFs. In this study, the positions and the orientations of the nexors are found by using the Denavit-Hartenberg parameters. This information gives where the joints are placed, how they are oriented and take position according to one another. Besides, the influence of engagement length on the fan height and the base edge are analyzed. Thereby one will be able to find out how much space the RF covers with the known base edge. With the geometric knowledge obtained from this study, demountable RFs having different engagement lengths can be produced with the same nexors.