Synthesis, Mobility, and Multifurcation of Deployable Polyhedral Mechanisms With Radially Reciprocating Motion

By Guowu Wei, Yao Chen, J. Dai. 2014

126 citations recorded by the source corpus.

Extending the method coined virtual-center-based (VCB) for synthesizing a group of deployable platonic mechanisms with radially reciprocating motion by implanting dual-plane-symmetric 8-bar linkages into the platonic polyhedron bases, this paper proposes for the first time a more general single-plane-symmetric 8-bar linkage and applies it together with the dual-plane-symmetric 8-bar linkage to the synthesis of a family of one-degree of freedom (DOF) highly overconstrained deployable polyhedral mechanisms (DPMs) with radially reciprocating motion. The two 8-bar linkages are compared, and geometry and kinematics of the single-plane-symmetric 8-bar linkage are investigated providing geometric constraints for synthesizing the DPMs. Based on synthesis of the regular DPMs, synthesis of semiregular and Johnson DPMs is implemented, which is illustrated by the synthesis and construction of a deployable rectangular prismatic mechanism and a truncated icosahedral (C60) mechanism. Geometric parameters and number synthesis of typical semiregular and Johnson DPMs based on the Archimedean polyhedrons, prisms and Johnson polyhedrons are presented. Further, movability of the mechanisms is evaluated using symmetry-extended rule, and mobility of the mechanisms is verified with screw-loop equation method; in addition, degree of overconstraint of the mechanisms is investigated by combining the Euler's formula for polyhedrons and the Grubler–Kutzbach formula for mobility analysis of linkages. Ultimately, singular configurations of the mechanisms are revealed and multifurcation of the DPMs is identified. The paper hence presents an intuitive and efficient approach for synthesizing PDMs that have great potential applications in the fields of architecture, manufacturing, robotics, space exploration, and molecule research.

Subfields: Civil and Structural Engineering, Control and Systems Engineering, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/5d65049a0f3483c295c3b4cb7a264f14f55843d5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

1. Jian Feng
2. Yao Chen
3. Pooya Sareh

In Control and Systems Engineering

1. Jian Feng
2. Yao Chen
3. Pooya Sareh

In Mechanical Engineering

1. Jian Feng
2. Yao Chen
3. Pooya Sareh

Citations in the corpus

• Effective insights into the geometric stability of symmetric skeletal structures under symmetric variations (2015, background): “In addition, group theory can be extended to analyze the mobility and geometric stability of finite mechanisms (Zhao et al., 2009; Ding et al., 2011; Wei et al., 2014; Wei and Dai, 2014) that were explored with screw theory.”