Geometric construction and reconfiguration analysis of multi-mode two-loop spatial mechanisms and their multi-loop extensions

Multi-mode multi-loop spatial mechanisms (MMSMs) are an important class of reconfigurable mechanisms, yet their diversity remains highly limited. This paper focuses on the geometric construction and reconfiguration analysis of multi-mode two-loop spatial mechanisms (MTSMs) and their extensions to MMSMs. Using the construction method, three types of MTSMs with two motion modes are synthesized by combining two classical Bricard mechanisms while constraining their undesired motion modes. Reconfiguration analysis of the proposed MTSMs is conducted using dual quaternions and the natural exponential function substitution to prove their motion characteristics. Subsequently, the construction method is extended to synthesize novel MMSMs with two motion modes. Various MMSMs are formed and further adopted to construct double-layer MMSMs for multi-mode morphing wings. Finally, the mobility properties of the double-layer MMSMs in both the contraction-expansion and parallelogram modes are substantiated through dual quaternions. This work provides a novel idea for constructing MMSMs from MTSMs without altering their motion characteristics.