Mobility analysis of tripod scissor structures using screw theory

Mechanisms consisting of spatial scissor units have different kinematic behaviors than those of planar scissors. However, their kinematics, especially the mobility analysis, has not received enough attention. Two types of deployable assemblies are analyzed in this paper, namely the translational and mirrored assemblies. Both the assemblies are made of tripod scissor units, and their instantaneous mobility are examined using screw theory. The study starts on the configuration where all the members have the identical deployment angle. Firstly, the geometric property of each assembly was studied. Then, screw-loop equations were developed based on graph theory and closure equations. Finally, the mobility of each assembly was computed using linear algebra. Following the analysis, physical prototypes were constructed to validate the results, and several different motion modes were obtained for the translational assembly. The analysis reveals different kinematic behaviors of the two assemblies. In the given configuration, the translational assemblies have four instantaneous degrees of freedom, while the mirrored assemblies have only a single instantaneous degree of freedom.