Vibration Analysis of a New Type of Compliant Mechanism with Flexible-Link, Using Perturbation Theory

Vibration analysis of a new type of compliant parallel mechanism with flexible intermediate links is investigated. The application of the Timoshenko beam theory to the mathematical modeling of the intermediate flexible link is described, and the equations of motion of the flexible links are obtained by using Lagrange’s equation of motion. The equations of motion are obtained in the form of a set of ordinary differential equations by using assumed mode method theory. The governing differential equations of motion are solved using perturbation method. The assumed mode shapes and frequencies are to be obtained based on clamped-clamped boundary conditions. Comparing perturbation method with Runge-Kutta-Fehlberg 4, 5th leads to highly accurate solutions, and the results are performed and discussed

FlexDelta: A flexure-based fully decoupled parallel xyzxyz positioning stage with long stroke

Decoupled parallel $xyz$ positioning stages with large stroke have been desired in high-speed and precise positioning fields. However, currently such stages are either short in stroke or unqualified in parasitic motion and coupling rate. This paper proposes a novel flexure-based decoupled parallel $xyz$ positioning stage (FlexDelta) and conducts its conceptual design, modeling, and experimental study. Firstly, the working principle of FlexDelta is introduced, followed by its mechanism design with flexure. Secondly, the stiffness model of flexure is established via matrix-based Castigliano's second theorem, and the influence of its lateral stiffness on the stiffness model of FlexDelta is comprehensively investigated and then optimally designed. Finally, experimental study was carried out based on the prototype fabricated. The results reveal that the positioning stage features centimeter-stroke in three axes, with coupling rate less than 0.53%, parasitic motion less than 1.72 mrad over full range. And its natural frequencies are 20.8 Hz, 20.8 Hz, and 22.4 Hz for $x$, $y$, and $z$ axis respectively. Multi-axis path tracking tests were also carried out, which validates its dynamic performance with micrometer error

A method for the mechatronico analysis of parallel kinematics manipulators based on decoupling the dynamics of actuators and mechanism

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Creative design and modelling of large-range translation compliant parallel manipulators

Compliant parallel mechanisms/manipulators (CPMs) are parallel manipulators that transmit motion/load by deformation of their compliant members. Due to their merits such as the eliminated backlash and friction, no need for lubrication, reduced wear and noise, and monolithic configuration, they have been used in many emerging applications as scanning tables, bio-cell injectors, nano-positioners, and etc. How to design large-range CPMs is still a challenging issue. To meet the needs for large-range translational CPMs for high-precision motion stages, this thesis focuses on the systematic conceptual design and modelling of large-range translational CPMs with distributed-compliance. Firstly, several compliant parallel modules with distributed-compliance, such as spatial multi-beam modules, are identified as building blocks of translational CPMs. A normalized, nonlinear and analytical model is then derived for the spatial multi-beam modules to address the non-linearity of load-equilibrium equations. Secondly, a new design methodology for translational CPMs is presented. The main characteristic of the proposed design approach is not only to replace kinematic joints as in the literature, but also to replace kinematic chains with appropriate multiple degrees-of-freedom (DOF) compliant parallel modules. Thirdly, novel large-range translational CPMs are constructed using the proposed design methodology and identified compliant parallel modules. The proposed novel CPMs include, for example, a 1-DOF compliant parallel gripper with auto-adaptive grasping function, a stiffness-enhanced XY CPM with a spatial compliant leg, and an improved modular XYZ CPM using identical spatial double four-beam modules. Especially, the proposed XY CPM and XYZ CPM can achieve a 10mm’s motion range along each axis in the case studies. Finally, kinematostatic modelling of the proposed translational CPMs is presented to enable rapid performance characteristic analysis. The proposed analytical models are also compared with finite element analysis