Mobility analysis of a 3-PUU flexure-based manipulator based on screw theory and compliance matrix method

2013 ◽  
Vol 14 (8) ◽  
pp. 1345-1353 ◽  
Author(s):  
Shunli Xiao ◽  
Yangmin Li ◽  
Qiaoling Meng
2019 ◽  
Vol 90 (4) ◽  
pp. 045102 ◽  
Author(s):  
Hongtao Yu ◽  
Chi Zhang ◽  
Bao Yang ◽  
Si-Lu Chen ◽  
Zaojun Fang ◽  
...  

Author(s):  
Nianfeng Wang ◽  
Zhiyuan Zhang ◽  
Xianmin Zhang

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.


Actuators ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 200
Author(s):  
Xiaofeng Yang ◽  
Jinyan Tang ◽  
Wenxin Guo ◽  
Hu Huang ◽  
Haoyin Fan ◽  
...  

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.


Author(s):  
Werner W. P. J. van de Sande ◽  
Just L. Herder

Parasitic motion is undesired in precision mechanisms, it causes unwanted kinematics. These erroneous motions are especially apparent in compliant mechanisms. Usually an analysis of parasitic motion is only valid for one type of mechanism. Kinematic information is imbedded in the compliance matrix of any mechanism; an eigenscrew decomposition expresses this kinematic information as screws. It uses screw theory to identify the lines along which a force yields a parallel translation and a rotation yields a parallel moment. These lines are called eigenwrenches and eigentwists. Any other load on the compliant mechanism will lead to parasitic motion. This article introduces two parasitic motion metrics using eigenscrew decomposition: the parasitic resultant from an applied screw and the deviation of an actual degree of freedom from a desired degree of freedom. These metrics are applicable to all compliant mechanism and allow comparison between two compliant mechanisms. These metrics are applied to some common compliant mechanisms as an example.


Author(s):  
Zhen Huang ◽  
Si J. Zhu

This paper presents the kinematic analyses of a 5-DOF 3-RCRR parallel mechanism. The end-effector of this mechanism can rotate round rotation center and one reference point on it can translate in a plane parallels to the base platform. Since the traditional Kutzbach-Gru¨bler formula is not valid for this mechanism, the modified Kutzbach-Gru¨bler formula and screw theory are used in the mobility analysis. The Duffy’s spherical analytic theory is used in forward/reverse position analyses. In forward/reverse velocity/acceleration analyses, virtual mechanism principle is used to build a virtual parallel mechanism (3-PvRCRR), which is equivalent to the initial mechanism (3-RCRR) on kinematics if all rates of virtual pairs (Pv) are set to be zero. At the end, some kinematics curves are presented with a numerical example.


2016 ◽  
Vol 9 (1) ◽  
Author(s):  
Wen-ao Cao ◽  
Huafeng Ding ◽  
Donghao Yang

This paper presents an approach to compliance modeling of three-translation and two-rotation (3T2R) overconstrained parallel manipulators, especially for those with multilink and multijoint limbs. The expressions of applied wrenches (forces/torques) exerted on joints are solved with few static equilibrium equations based on screw theory. A systematic method is proposed for deriving the stiffness model of a limb with considering the couplings between the stiffness along the constrained wrench and the one along the actuated wrench based on strain energy analysis. The compliance model of a 3T2R overconstrained parallel mechanism is established based on stiffness models of limbs and the static equilibrium equation of the moving platform. Comparisons show that the compliance matrix obtained from the method is close to the one obtained from a finite-element analysis (FEA) model. The proposed method has the characteristics of involving low computational efforts and considering stiffness couplings of each limb.


Author(s):  
Qinchuan Li ◽  
Xudong Hu ◽  
Zhen Huang

This paper presents a method for the Jacobian derivation of 5-DOF 3R2T PMs (parallel mechanisms), where 3R denotes three rotational DOFs (degrees of freedom) and 2T denotes two translational DOFs. First the mobility analysis of such kind of parallel mechanisms is reviewed briefly. The Jacobian matrix of the single limb kinematic chain is obtained via screw theory, which is a 6 × 5 matrix. Then it is shown that the mobility analysis of such kind of PM is important when simplifying the 6 × 5 matrix into a 5 × 5 Jacobian matrix. After obtaining the 5 × 5 Jacobian matrix for each limb, a 5 × 5 Jacobian matrix for the whole mechanism can be established.


Author(s):  
C. Qiu ◽  
J. J. Yu ◽  
S. Z. Li ◽  
Hai-jun Su ◽  
Y. Z. Zeng

This paper introduces an approach for synthesis of actuation spaces of multi-axis parallel flexure mechanisms. The concept of actuation space, first proposed by J. Hopkins and M. Culpepper, is developed from constraint and freedom space, which are two fundamental concepts in constraint-based method. Within the framework of screw theory, actuation and constraint can be represented mathematically by a wrench, and freedom can be depicted by a twist. A Compliance matrix is provided to set the relationship between constraint wrenches and actuation forces in view that such an important rule as “actuation forces are linear independent of constraint wrenches”. Developed from this design rule, a synthesis criterion of actuation space of flexure systems is promoted to select suitable actuators. As a result, this synthesis criterion enable designers to (i) formulate the actuation space systematically in the format of screws or screw system, (ii) determine actuator placement according to the requirement of minimizing the interference between actuation forces and constraint wrenches. Synthesis procedures and selective examples are discussed in details.


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