The design and kinetostatic modeling of 3PPR planar compliant parallel mechanism based on compliance matrix method

2019 ◽  
Vol 90 (4) ◽  
pp. 045102 ◽  
Author(s):  
Hongtao Yu ◽  
Chi Zhang ◽  
Bao Yang ◽  
Si-Lu Chen ◽  
Zaojun Fang ◽  
...  
Keyword(s):  
Matrix Method ◽  
Parallel Mechanism ◽  
Compliance Matrix ◽  
Compliant Parallel Mechanism ◽  
Compliance Matrix Method

A Quasi-Static Model for Planar Compliant Parallel Mechanisms

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Cyril Quennouelle ◽  
Clément Gosselin
Keyword(s):  
Parallel Mechanism ◽  
Applied Load ◽  
Jacobian Matrix ◽  
Static Model ◽  
Parallel Mechanisms ◽  
Compliance Matrix ◽  
End Effector ◽  
Kinematic Constraints ◽  
Compliant Parallel Mechanism ◽  
External Loads

In this paper, the mobility, the kinematic constraints, the pose of the end-effector, and the static constraints that lead to the kinematostatic model of a compliant parallel mechanism are introduced. A formulation is then provided for its instantaneous variation—the quasi-static model. This new model allows the calculation of the variation in the pose as a linear function of the motion of the actuators and the variation in the external loads through two new matrices: the compliant Jacobian matrix and the Cartesian compliance matrix that give a simple and meaningful formulation of the model of the mechanism. Finally, a simple application to a planar four-bar mechanism is presented to illustrate the use of this model and the new possibilities that it opens, notably the study of the kinematics for any range of applied load.

Stiffness analysis of corrugated flexure beam using stiffness matrix method

2018 ◽  
Vol 233 (5) ◽  
pp. 1818-1827 ◽  
Author(s):  
Nianfeng Wang ◽  
Zhiyuan Zhang ◽  
Xianmin Zhang
Keyword(s):  
Stiffness Matrix ◽  
Matrix Method ◽  
Beam Theory ◽  
Analytical Models ◽  
The Finite Element Method ◽  
Compliance Matrix ◽  
Stiffness Analysis ◽  
Compliance Matrix Method ◽  
Euler Bernoulli Beam ◽  
The Relationship

Precision positioning techniques present a significant opportunity to support the instrumentation development for state-of-the-art micro-positioning research. The requirement of large stroke and high resolution of the mechanism without a need for amplifier mechanisms is universally recognized. Corrugated flexure beam can have some potential if designed right because of its large flexibility obtained from longer overall length on the same span. This paper presents stiffness analysis of corrugated flexure beam using stiffness or compliance matrix method. Based on Euler–Bernoulli beam theory and Mohr’s integral method, the deformation analyses of straight segment and semi-circle segment are presented. And the stiffness matrix of corrugated flexure unit is then obtained via transformation matrix. By combining the stiffness matrix of every single corrugated flexure unit, the stiffness matrix of corrugated flexure beam is delivered, which reflects the relationship between the load and displacement. The analytical models are verified by taking advantage of the finite element method, which shows that all the results can be of considerable use in the design of corrugated flexure beam.

scholarly journals Design and Analysis of a Stepping Piezoelectric Actuator Free of Backward Motion

Actuators ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 200
Author(s):  
Xiaofeng Yang ◽  
Jinyan Tang ◽  
Wenxin Guo ◽  
Hu Huang ◽  
Haoyin Fan ◽  
...  
Keyword(s):  
Piezoelectric Actuator ◽  
Matrix Method ◽  
Piezoelectric Actuators ◽  
Flexure Hinge ◽  
Compliance Matrix ◽  
Stick Slip ◽  
New Strategy ◽  
Piezoelectric Stacks ◽  
Compliance Matrix Method ◽  
Phase Differences

Although the stick-slip principle has been widely employed for designing piezoelectric actuators, there still exits an intrinsic drawback, i.e., the backward motion, which significantly affects its output performances and applications. By analyzing the generation mechanism of backward motion in stick-slip piezoelectric actuators, the elliptical trajectory was employed to design a novel stepping piezoelectric actuator free of backward motion. Accordingly, a prototype of piezoelectric actuator was designed, which utilized a flexure hinge mechanism and two vertically arranged piezoelectric stacks to generate the required elliptical trajectory. The compliance matrix method was used to theoretically analyze the flexure hinge mechanism. The theoretical and measured elliptical trajectories under various phase differences were compared, and the phase difference of 45° was selected accordingly. Under a critical relative gap, output performances of the actuator working under the elliptical trajectory were characterized, and then compared with that obtained under the normal stick-slip driving principle. Experimental results indicated that forward and reverse stepping displacement with completely suppressed backward motion could be achieved when employing the elliptical trajectory, verifying its feasibility. This study provides a new strategy for designing a stepping piezoelectric actuator free of backward motion.

scholarly journals Design and DOF Analysis of a Novel Compliant Parallel Mechanism for Large Load

Sensors ◽  
2019 ◽  
Vol 19 (4) ◽  
pp. 828 ◽  
Author(s):  
Xiaochuan Wu ◽  
Yi Lu ◽  
Xuechao Duan ◽  
Dan Zhang ◽  
Wenyao Deng
Keyword(s):  
Finite Element ◽  
Parallel Mechanism ◽  
Screw Theory ◽  
Load Capacity ◽  
Spherical Joint ◽  
Analysis Model ◽  
Compliance Matrix ◽  
Large Load ◽  
Compliant Parallel Mechanism ◽  
Six Dof

The degree of freedom (DOF) and motion characteristics of a kind of compliant spherical joint were analyzed based on the screw theory, and a new design scheme for force-inversion of the compliant spherical joint was proposed in this paper. A novel type of six DOF compliant parallel mechanism (CPM) was designed based on this scheme to provide a large load capacity and achieve micrometer-level positioning accuracy. The compliance matrix of the new type of CPM was obtained through matrix transformation and was then decomposed into its generalized eigenvalues. Then, the DOF of the mechanism was numerically analyzed based on the symbolic formulation. The finite element analysis model of the compliant parallel mechanism was established. The static load analysis was used to verify the large load capacity of the mobile platform. By comparing the deformation obtained by the compliance matrix numerical method with the deformation obtained by the finite element method, the correctness of the compliance matrix and the number of the DOF of the CPM was verified.

Realization of an Arbitrary Elastic Behavior With an Elastic Mechanism Having Concurrent Axes

2000 ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
Elastic Behavior ◽  
Unique Point ◽  
Compliance Matrix ◽  
Elastic Mechanism ◽  
Serial Mechanism

Abstract In this paper, synthesis of an arbitrary elastic behavior with an elastic mechanism is addressed. The mechanisms considered are parallel and serial mechanisms with concurrent axes. We show that any stiffness matrix can be realized through a parallel mechanism with all spring axes intersecting at a unique point. This point is shown to be the center of stiffness. We also show that any compliance matrix can be realized through a serial mechanism with all joint axes intersecting at a unique point. This point is shown to be the center of compliance. Synthesis procedures for mechanisms with these properties are provided.

Experimental Validation of the Kinematics of a 3PRS Compliant Mechanism for Micromilling

2015 ◽  
Author(s):  
Antonio Ruiz ◽  
Francisco Campa Gomez ◽  
Constantino Roldan-Paraponiaris ◽  
Oscar Altuzarra
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Experimental Validation ◽  
Compliant Mechanism ◽  
Motion Controller ◽  
End Effector ◽  
Compliant Joints ◽  
Hybrid Manipulator ◽  
Compliant Parallel Mechanism ◽  
Actuated Joints

The present work deals with the development of a hybrid manipulator of 5 degrees of freedom for milling moulds for microlenses. The manipulator is based on a XY stage under a 3PRS compliant parallel mechanism. The mechanism takes advantage of the compliant joints to achieve higher repetitiveness, smoother motion and a higher bandwidth, due to the high precision demanded from the process, under 0.1 micrometers. This work is focused on the kinematics of the compliant stage of the hybrid manipulator. First, an analysis of the workspace required for the milling of a single mould has been performed, calculating the displacements required in X, Y, Z axis as well as two relative rotations between the tool and the workpiece from a programmed toolpath. Then, the 3PRS compliant parallel mechanism has been designed using FEM with the objective of being stiff enough to support the cutting forces from the micromilling, but flexible enough in the revolution and spherical compliant joints to provide the displacements needed. Finally, a prototype of the 3PRS compliant mechanism has been built, implementing a motion controller to perform translations in Z direction and two rotations. The resulting displacements in the end effector and the actuated joints have been measured and compared with the FEM calculations and with the rigid body kinematics of the 3PRS.

Displacement Analysis of the 3SPS-3CCS Mechanism Based on Hyper-Chaotic Damp Least Square Method

2011 ◽  
Vol 55-57 ◽  
pp. 2092-2098
Author(s):  
You Xin Luo ◽  
Qi Yuan Liu ◽  
Xiao Yi Che ◽  
Bin Zeng
Keyword(s):  
Mathematical Model ◽  
Real Number ◽  
Matrix Method ◽  
Parallel Mechanism ◽  
Least Square Method ◽  
Least Square ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Chaotic Sequences ◽  
Chaos System

The forward displacement analysis of parallel mechanism is attributed to find the solutions of complicated nonlinear equations and it is a very difficult process. Taking chaotic sequences as the initial values of the damp least square method, we can find all the solutions of equations quickly. Making use of existing chaos system and discovering new chaos system to generate chaotic sequences with good properties is the key to the damp least square method based on Chaos sequences. Based on utilizing hyper-chaotic Hénon mapping to obtain initial points, a new method of finding all real number solutions of the nonlinear questions is proposed. Using cosine matrix method, the author established the mathematical model of forward displacement for the generalized 3SPS-3CCS parallel robot mechanism and a numerical example is given. Compared to the quaternion method building mathematical model, the result shows cosine matrix method building mathematical model and hyper-chaotic damp least square method to find solution is brief and high calculation efficiency as the calculation is done in real number range. The proposed method has universality which can be used in forward displacement of other parallel mechanism.

Spatial Compliances Achieved With Serial Elastic Mechanisms

2000 ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Rotational Motion ◽  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
Elastic System ◽  
Compliance Matrix ◽  
Elastic Joint ◽  
Compliant Behavior ◽  
Elastic Mechanism ◽  
Spatial Compliance ◽  
Serial Mechanism

Abstract Previously, the structure of a spatial stiffness matrix and its realization using a parallel elastic system have been addressed. This paper extends those results to the analysis and realization of a spatial compliance matrix using a serial mechanism. We show that, a spatial compliance matrix can be decomposed into a set of rank-1 primitive matrices, each of which can be realized with an elastic joint in a serial mechanism. To realize a general spatial compliance, the serial mechanism must contain joints that couple the translational and rotational motion along/about an axis. The structure of a spatial compliance matrix can be uniquely interpreted by a 6-joint serial elastic mechanism whose geometry is obtained from the eigenscrew decomposition of the compliance matrix. The results obtained from the analysis of spatial compliant behavior and its realization in a serial mechanism are compared with those obtained for spatial stiffness behavior and its realization in a parallel mechanism.

scholarly journals A Compliant-Parallel Mechanism with Bio-Inspired Compliant Joints for High Precision Assembly Robot

Procedia CIRP ◽  
2013 ◽  
Vol 5 ◽  
pp. 175-178 ◽  
Author(s):  
Hiroaki Kozuka ◽  
Jumpei Arata ◽  
Kenji Okuda ◽  
Akinori Onaga ◽  
Motoshi Ohno ◽  
...  
Keyword(s):  
High Precision ◽  
Parallel Mechanism ◽  
Compliant Joints ◽  
Compliant Parallel Mechanism
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