This article analyzes the singularities and workspace of two tensegrity mechanisms that employ a passive universal joint and either three or four tension springs. These two architectures are correlated to 3-SPS-U and 4-SPS-U parallel mechanisms for determining their geometric equations. By fixing the limits of prismatic joints, the workspace for the mechanisms is generated and the parallel singularities are analyzed. Based on the singularity boundaries obtained from the workspace, the joint limits are modified to generate the maximal singularity free workspaces for both the architectures. A comparison is done based on the tilt limits obtained from the workspace of the mechanisms. The mechanism with the maximum tilt limits is implemented for a piping inspection robot to pass through pipe bends and junctions.