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• The coupling-constraint properties of single-loop kirigami are investigated. • A synthesis method of 1-degree-of-freedom multi-loop kirigami is proposed. • The forward & inverse design method of kirigami meshes are proposed. Kirigami has been utilized in designing deployable mechanisms for various engineering applications. This paper presents a novel construction method for one-degree-of-freedom (1-DOF) multi-loop kirigami mechanisms whose folding motions are kinematically equivalent to their original degree-4 rigid origami. Firstly, we introduce a family of single-loop kirigami (SLK) as the main loop of 1-DOF multi-loop kirigami. Secondly, the coupling-constraint properties of multi-DOF SLKs are clarified, and the structural characteristics of the 1-DOF multi-loop kirigami are defined, based on which, the construction method for the 1-DOF multi-loop kirigami is proposed. Thirdly, the representative models are selected and their kinematics are presented to demonstrate their capability to achieve folding motion equivalent to their origami prototypes, thus verifying the validity of our proposed methodology. Fourthly, the non-constraint condition of the 1-DOF multi-loop kirigami is presented. Finally, we propose extended configurations of 1-DOF multi-loop kirigami and provide the forward and inverse design methods for constructing kirigami meshes. The proposed methodology facilitates the design of large-scale deployable structures. [ABSTRACT FROM AUTHOR]

• Instantaneous Kinematics (IK) of multi-DOF spatial mechanisms(SMs) is addressed • New geometric and analytic techniques for the analysis of this IK are presented • They relate multi-DOF SM's IK to the IK of the single-DOF SMs generated from it • They use Inst.-Screw-Axes (ISAs) and are implementable in a CAD system • The proposed methodology is relevant in mechanism design Multi-degree-of-freedom (multi-DOF) mechanisms generate single-DOF mechanisms by locking all their generalized coordinates but one. Here, the superposition principle is used to state a relationship between spatial multi-DOF mechanisms' instantaneous kinematics (IK) and the IK of the single-DOF mechanisms they generate. Firstly, the relationship between the instantaneous screw axes (ISAs) of a multi-DOF mechanism and the ISAs of the single-DOF mechanisms, it generates, is found; then, it is used for its singularity analysis. In particular, the IK model of a generic multi-DOF spatial mechanism is written through the ISA locations and, successively, it is studied to identify all the singular configurations of the multi-DOF mechanism through the analysis of the single-DOF mechanisms it generates. The results are a technique for the determination of ISAs' locations in multi-DOF spatial mechanisms and a singularity-analysis technique, for the same mechanism types, based on the singularity analysis of single-DOF spatial mechanisms. Eventually, the proposed techniques are applied to a case study. As far as this author is aware, both these results are presented for the first time in the literature. [ABSTRACT FROM AUTHOR]

• The mobility of mechanisms comprising spatial scissor units are analyzed. • The translational assembly has 4 DOFs, while the 4th DOF is infinitesimal. • The mirrored assembly has a single DOF and thus can be deployed in one mode. 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. [ABSTRACT FROM AUTHOR]

Parallel continuum mechanisms are a type of compliant mechanisms comprising a rigid end-effector connected to a fixed frame by flexible and slender elements in a closed-kinematic morphology, being their flexibility the source of mobility. Solving the position problem involves the static equilibrium of the whole device considering the nonlinear large deformations of slender elements. Numerical iterative solutions are already available to solve real-time simulations. However, an assembled solution, which meets both geometric conditions and static equilibrium, is needed to start the process. A comprehensive Kinematic Analysis in the classical sense is not fully established yet. The aim of the paper is to propose a procedure that solves the full inverse and forward kinematic problems for planar three degrees of freedom systems, hence obtaining the multiple solutions arising from the closed-loop structure and the multiplicity of the deformation mode of slender links. From those solutions, finding of the different aspects that comprise the workspace is possible, as well as determining singularities and instability loci. • To find multiple solutions of position problem of 3 DoF planar parallel continuum mechanisms. • Kirchhoff planar deformation rod model integrated using elliptic integrals. • Multiple solutions in association with variability of buckling modes. • Obtaining aspects of the workspace, singularities and instability loci. [ABSTRACT FROM AUTHOR]

A four degrees-of-freedom (DOF) Parallel Manipulator (PM) with a 4 P Pa-2PaR configuration has been proposed to generate 3-DOF Translational and 1-DOF Rotational (3T1R) motions in our early work. It has the advantages of symmetric geometry, simple kinematics and infinite extension of translational workspace along its linear guide direction. However, its V-type assembly mode results in a long distance between its moving platform and the base, which makes its stiffness and accuracy lower. Besides, its the other two translational workspaces are limited due to its kinematic singularities. To overcome such limitations, the PM is modified by utilizing its M-type assembly mode and placing an offset angle to the last parallelogram mechanism. To simplify the displacement analysis, a geometrical projection method is employed, while a closed-loop vector approach is used for its instantaneous kinematic analysis. Both singularity and workspace issues are investigated. An optimization algorithm based on Genetic Algorithm is proposed to maximize the reachable workspace. The optimization result indicates that the workspace is significantly increased. A prototype of the M-type PM is fabricated to validate the effectiveness of the modified design. • A modified 4-DOF 3T1R parallel manipulator with M-type assembly mode is proposed. • An offset angle is placed to the last parallelogram to enlarge the workspace. • A geometrical projection method is employed to simplify the kinematic analysis. • The workspace in x – o – z plane is significantly increased through design optimization. [ABSTRACT FROM AUTHOR]