A normalization-based approach to the mobility analysis of spatial compliant multi-beam modules

This paper presents a normalization-based approach to the mobility analysis of spatial compliant multi-beam modules to address the dimensional-inhomogeneity issue of motion/load. Firstly, two spatial non-tilted and tilted multi-beam modules, composed of uniform beams with symmetrical cross sections and same length, are proposed. Using a normalization technique, the compliance matrices of these spatial multi-beam modules are derived, from which the DOF (degrees-of-freedom) of the compliant modules can be obtained by direct observation and/or screw representation. The results are compared with those obtained without normalization. It is shown that the DOF of these compliant modules can be identified more easily using the proposed approach than the approach without normalization. Then, two spatial double non-tilted and tilted three-beam modules are proposed and analyzed for potential applications such as acting as building blocks of new compliant manipulators. The normalization-based approach can also be used for the mobility analysis of spatial compliant multi-sheet modules such as the parallelogram module and the four-sheet rotational module and the error analysis of spatial multi-beam modules with beams of compatible length.

► A normalization-based approach is proposed for the mobility analysis. ► Load–displacement modeling is performed for spatial multi-beam modules. ► Compliance matrices are analyzed to reflect the degrees-of-freedom. ► Several good compliant double modules are presented.