Dynamic Modeling and Analysis of a 3 PRS Parallel Mechanism Using Constrained Robotic Approach

Author(s):  
Meng-Shiun Tsai ◽  
Wei-Hsiung Yuan

In this paper, a novel model is developed to analyze a 3-PRS parallel mechanism. The 3-PRS mechanism consists of a moving platform which is manipulated by three actuated fingers. Since the fingertips are constrained by the moving platform, three holonomic constraint equations are derived and the associated constraint forces are studied based on the theory of differential geometry. The developed model could be utilized to separate the dynamics of the fingers and that of the moving platform such that the coupling behaviors of the fingers can be investigated. It is found that the reaction forces applied at the fingertips of the parallel manipulator include not only the driving forces to the moving platform but also the constraint forces. Besides, the constraint forces are determined to be internal forces which would not generate a net force or torque to drive the moving platform. Simulations are performed to study the dynamic behavior of the reaction forces and it is found that the constraint forces have significant effect on the actuated fingers.

Robotics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 66
Author(s):  
Maurizio Ruggiu ◽  
Xianwen Kong

This paper deals with the reconfiguration analysis of a 3-DOF (degrees-of-freedom) parallel manipulator (PM) which belongs to the cylindrical parallel mechanisms family. The PM is composed of a base and a moving platform shaped as equilateral triangles connected by three serial kinematic chains (legs). Two legs are composed of two universal (U) joints connected by a prismatic (P) joint. The third leg is composed of a revolute (R) joint connected to the base, a prismatic joint and universal joint in sequence. A set of constraint equations of the 1-RPU−2-UPU PM is derived and solved in terms of the Euler parameter quaternion (a.k.a. Euler-Rodrigues quaternion) representing the orientation of the moving platform and of the Cartesian coordinates of the reference point on the moving platform. It is found that the PM may undergo either the 3-DOF PPR or the 3-DOF planar operation mode only when the base and the moving platform are identical. The transition configuration between the operation modes is also identified.


Author(s):  
D Gan ◽  
Q Liao ◽  
J S Dai ◽  
S Wei ◽  
L D Seneviratne

A new parallel mechanism 1CCC–5SPS which has distance and angle constraints is introduced in this article. Degree of freedom and forward kinematic analysis of this new parallel mechanism are presented, in which four equivalent polynomial equations are obtained from the original six geometrical constraint equations. The Gröbner basis theory is used with the four equations and the problem of forward displacement is reduced to a 40th degree polynomial equation in a single unknown from a constructed 10 × 10 Sylvester's matrix which is small in size, from which 40 different locations of the moving platform can be derived. A numerical example confirms the efficiency of the procedure.


2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Latifah Nurahmi ◽  
Dongming Gan

Abstract This paper focuses on the reconfiguration of a 3-(rR)PS metamorphic parallel mechanism based on complete workspace and operation mode analysis. The mechanism consists of three (rR)PS legs, and each (rR) joint is composed of two perpendicular revolute joints. One of the (rR) joint axes can be reconfigured continuously, which allows the mechanism to exhibit three distinct configurations. Initially, the constraint equations are derived by using algebraic geometry approach, and the primary decomposition is computed for the three configurations. It reveals that the 3-(rR)PS metamorphic parallel mechanism can exhibit one up to two operation modes among three configurations. When the second axes of the three (rR) joints intersect at a finite point and not coplanar, the 3-(rR)PS metamorphic parallel mechanism has only one operation mode. If the second axes of the three (rR) joints are coplanar, the 3-(rR)PS metamorphic parallel mechanism has two operation modes. It is shown that both operation modes have the same motion type, namely, 1T2R motion. However, to realize the same trajectories in both operation modes, the moving platform will have different orientations. Hence, the orientation workspaces of both operation modes are characterized and the axodes are used to compare the instantaneous motion of the moving platform when passing through the same trajectories. Based on these results, an identification approach is introduced to identify which operation mode a given mechanism pose belongs to and this provides a useful method for trajectory planning.


2009 ◽  
Vol 31 (1) ◽  
pp. 57-64
Author(s):  
Do Sanh ◽  
Dinh Van Phong ◽  
Do Dang Khoa ◽  
Phan Dang Phong

In the paper, it is introduced a method to determine joint reaction forces, constraint forces and internal forces at the cross section of linkages. Based on the principle of compatibility and the ideality of constraints, the methodology is presented to analyze and determine reaction forces in planar mechanisms.


Author(s):  
Shihua Li ◽  
Zhen Huang ◽  
Jianguang Wu

In order to enrich deficient-DOF parallel mechanism models, a novel model of a 3-DOF platform manipulator is presented and establish its inverse kinematics equation. Here, studies instantaneous motions of 3-RRRRR parallel manipulator at initial configuration and general configuration. Find: it has three degrees of freedom at initial configuration and after translated along the X, Y, Z axis. Secondly, the relation is given between every active input (θ1) and moving platform position by using D-H means, the solution is developed for inverse kinematics, numerical example for the position kinematic is presented, the figure of workspace along the Z-axis is drawn finally. The mechanism can be applied to jiggle mechanism.


2017 ◽  
Vol 41 (5) ◽  
pp. 922-935
Author(s):  
HongJun San ◽  
JunSong Lei ◽  
JiuPeng Chen ◽  
ZhengMing Xiao ◽  
JunJie Zhao

In this paper, a 3-DOF translational parallel mechanism with parallelogram linkage was studied. According to the space vector relation between the moving platform and the fixed base, the direct and inverse position solutions of this mechanism was deduced through analytical method. In addition, the error of the algorithm was analyzed, and the algorithm had turned out to be effective and to have the satisfactory computational precision. On the above basis, the workspace of this mechanism was found through graphical method, which was compared with that of finding through Monte Carlo method, and there was the feasibility for analyzing the workspace of the mechanism by graphical method. The characteristic of the mechanism was analyzed by comparing the results of two analysis methods, which provided a theoretical basis for the application of the mechanism.


Author(s):  
Alessandro Cammarata ◽  
Rosario Sinatra

This paper presents kinematic and dynamic analyses of a two-degree-of-freedom pointing parallel mechanism. The mechanism consists of a moving platform, connected to a fixed platform by two legs of type PUS (prismatic-universal-spherical). At first a simplified kinematic model of the pointing mechanism is introduced. Based on this proposed model, the dynamics equations of the system using the Natural Orthogonal Complement method are developed. Numerical examples of the inverse dynamics results are presented by numerical simulation.


2013 ◽  
Vol 579-580 ◽  
pp. 659-664
Author(s):  
Xiang Bo Ouyang ◽  
Ke Tian Li ◽  
Hong Jian Xia ◽  
Su Juan Wang ◽  
Huan Wei Zhou ◽  
...  

t presents the parallel mechanism and variable acceleration control method, which is composed of slider, connecting rod, moving platform and linear guide etc. The motion platform is supported by three connecting rods through hinging, the other end of the connecting rods are respectively hinged with two sliders. Among them two pairs of connecting rod, two sliders and the moving platform formed a symmetric structure that is the so called Parallel Mechanism. The third connecting rod is parallel to one of two connecting rods, so that the two parallel connecting rods, slide block and the moving platform formed a parallelogram structure, it makes that the moving platform is always parallel to liner guiderail in the process of movement. By controlling the two sliders moving in the way of variable acceleration, it can make the trajectory curve, speed curve and acceleration curve of the moving platform are continuous, smooth, so impact and vibration of the moving platform is limited in the operation process.


Author(s):  
Karsten Friis

Abstract How can we best analyze security subregions? The most commonly used theory of regional security in the discipline of international relations, the regional security complex theory, focuses on large regions, such as Europe, Asia, or the Middle East. It pays less attention to smaller regions within these. This is unfortunate, because the security dynamics of these subregions often are a result of more than their place in the larger region. At the same time, the security of subregions cannot be reduced to a function of the policies of the states comprising them either. In short, security subregions are a level of analysis in their own right, with their own material, ideational, economic, and political dynamics. To capture and understand this, we need an analytical framework that can be applied to security regions irrespective of where and when in time they occur. The aim of this article is to offer such an analytical framework that helps us theorize the forces forging regional security cooperation, by combining external push and pull forces with internal forces of pull and resistance. The utility of the framework is illustrated through the case of Nordic security cooperation. It allows for a systematic mapping of the driving forces behind it and the negative forces resisting it. The Nordic region thus becomes a meeting point between global and national forces, pushing and pulling in different directions, with Nordic Defense Cooperation being formed in the squeeze between them. Extrait Comment pouvons-nous analyser au mieux les sous-régions de sécurité? La théorie de sécurité régionale la plus communément exploitée dans la discipline des relations internationales, celle du complexe de sécurité régionale, se concentre sur de grandes régions, telles que l'Europe, l'Asie ou le Moyen-Orient. Elle accorde moins d'attention aux plus petites régions qui les constituent. Cela est regrettable, car les dynamiques de sécurité de ces sous-régions résultent souvent de bien d'autres facteurs que leur place dans la région. Dans le même temps, la sécurité des sous-régions ne peut pas non plus être réduite à une fonction des politiques des États qui les composent. En bref, les sous-régions de sécurité sont un niveau d'analyse à part entière, avec ses propres dynamiques matérielles, idéationnelles, économiques et politiques. Pour capturer et comprendre cela, nous avons besoin d'un cadre analytique pouvant être appliqué aux régions de sécurité, quels que soient le moment et le lieu où elles interviennent. Le but de cet article est de proposer un tel cadre analytique qui nous aide à théoriser les forces forgeant la coopération régionale de sécurité en alliant des forces externes de poussée et de traction à des forces internes de traction et de résistance. L'utilité de ce cadre est illustrée par le cas de la coopération de sécurité nordique. Il permet une cartographie systématique des forces motrices sur lesquelles elle repose et des forces négatives qui y résistent. La région nordique devient ainsi un point de rencontre entre forces nationales et internationales qui poussent et tirent dans différentes directions, la coopération de défense nordique se formant dans l'intervalle ainsi constitué. Resumen ¿Cuál es la mejor forma de analizar las subregiones de seguridad? La teoría sobre seguridad regional de uso generalizado en la disciplina de relaciones internacionales, la llamada Teoría de Complejos de Seguridad Regional, se centra principalmente en grandes regiones como Europa, Asia y el Medio Oriente y presta menos atención a regiones más pequeñas dentro ellas. Este aspecto es desafortunado, ya que la dinámica de seguridad de estas subregiones suele ser el resultado de otros factores además del lugar que ocupan dentro de estas regiones más grandes. Asimismo, la seguridad subregional tampoco puede reducirse a una función de las políticas de los estados que integran. En conclusión, las subregiones de seguridad merecen un nivel de análisis propio, con sus propias dinámicas materiales, conceptuales, económicas y políticas. Para captar y comprender esto, es necesario un marco analítico que pueda aplicarse a regiones de seguridad independientemente del lugar y el momento en el que suceden. Este artículo tiene como objetivo ofrecer ese marco analítico que ayude a teorizar los factores que forjan la cooperación de seguridad nacional al combinar factores externos de tensión y conciliación con factores internos de conciliación y resistencia. La utilidad del marco se explica a través del caso de la cooperación de seguridad nórdica. Permite realizar un mapeo sistemático de los factores subyacentes de impulso y los factores negativos de resistencia. La región nórdica, por tanto, se convierte en un punto de encuentro de los factores internacionales y nacionales de tensión y conciliación en distintas direcciones, y en el cual que se forma la cooperación nórdica de defensa.


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