Simulation and computer-aided kinematic design of three-degree-of-freedom spherical parallel manipulators (original) (raw)
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A novel design for three degree of freedom (DoF) mechanical arm, i.e. a 3-PUS/S Spherical Parallel Manipulator (SPM) with three rotational motions is proposed in this article. In addition, its kinematic equations, singularity and design optimization are studied according to its application. The proposed parallel robot that has three legs with three prismatic joints can rotate about Z-axis unlimitedly. Therefore, the manipulator has large workspace and good flexibility, hence being attractive to study. To complete the kinematic analysis of the manipulator, three stages are considered as follows. At the first, the kinematics of the SPM is explained to obtain the positions, velocities, and accelerations. Furthermore, the Jacobian and Hessian matrices of the 3-PUS/S Parallel Manipulator are derived. The results are verified by the use of CAD and Adams software. Next, the Jacobian matrix obtained from the kinematic equations is utilized to study the different types of singularities. Finally, the optimum dimensions of the manipulator based on kinematic and singularity features are studied by Genetic Algorithm (GA), and the Global Condition Index (GCI) is maximized. The results help the designers to achieve an ideal geometry for the parallel manipulator with good workspace and minimum singularity.
Analysis of Kinematics and Reconfigurability of a Spherical Parallel Manipulator
IEEE Transactions on Robotics, 2014
This article presents the kinematic characterization of a 3-CPU parallel manipulator designed for motions of pure rotation. The machine has been conceived at the Polytechnic University of Marche and recent studies have shown that its kinematic architecture can be exploited for the realization of reconfigurable machines with different kinds of motions (pure rotational, pure translational and planar motions among others). The 3-CPU concept has been subject to further investigations for a deeper understanding of this peculiar behaviour. After a brief introduction to these concepts, the paper faces the position and the differential kinematics of the 3-CPU spherical manipulator aiming at identifying workspace boundaries and its kinematic manipulability.
Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors
22nd Biennial Mechanisms Conference: Robotics, Spatial Mechanisms, and Mechanical Systems
In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of t...
Journal of Mechanisms and Robotics, 2015
This paper presents a new kinematics model for linear-actuated symmetrical spherical parallel manipulators (LASSPMs) which are commonly used considering their symmetrical kinematics and dynamics properties. The model has significant advantages in solving the forward kinematic equations, and in analytically obtaining singularity loci and the singularity-free workspace. The Cayley formula, including the three Rodriguez–Hamilton parameters from a general rotation matrix, is provided and used in describing the rotation motion and geometric constraints of LASSPMs. Analytical solutions of the forward kinematic equations are obtained. Then singularity loci are derived, and represented in a new coordinate system with the three Rodriguez–Hamilton parameters assigned in three perpendicular directions. Limb-actuation singularity loci are illustrated and forward kinematics (FK) solution distribution in the singularity-free zones is discussed. Based on this analysis, unique forward kinematic sol...
Kinematics of the 3(RPSP)-S Fully Spherical Parallel Manipulator by Means of Screw Theory
Robotics, 2018
In this work, the kinematics of a spherical parallel manipulator composed of three peripheral limbs equipped with linear actuators and a passive center shaft is approached by means of the theory of screws. The displacement analysis is carried out solving closure equations, which are obtained upon simple linear combinations of the components of two unit vectors describing the orientation of the moving platform. After, the input-output equations of velocity and acceleration of the spherical parallel manipulator are systematically obtained by resorting to reciprocal-screw theory. This strategy avoids the computation of the passive joint velocity and acceleration rates of the robot manipulator. Numerical examples illustrate the efficiency of the proposed method.
On the Kinematic Analysis of a Spatial Six-Degree-of-Freedom Parallel Manipulator
Scientia Iranica
In this paper, a novel spatial six-degree-of freedom parallel manipulator actuated by three base-mounted partial spherical actuators is studied. This new parallel manipulator consists of a base platform and a moving platform, which are connected by three legs. Each leg of the manipulator is composed of a spherical joint, prismatic joint and universal joint. The base-mounted partial spherical actuators can only specify the direction of their corresponding legs. In other words, the spin of each leg is a passive degree-of-freedom. The inverse pose and forward pose of the new mechanism are described. In the inverse pose kinematics, active joint variables are calculated with no need for evaluation of the passive joint variables. To solve the forward pose problem, a much simpler method compared to the traditional method is introduced. Closed form relations for the inverse and forward rate kinematics are proposed. Finally, two sets of singular connguration of the newly introduced manipulat...
Dynamic modeling and design optimization of a 3-DOF spherical parallel manipulator
2014
This paper deals with the dynamic modeling and design optimization of a three Degree-of-Freedom spherical parallel manipulator. Using the method of Lagrange multipliers, the equation of motion is derived by considering its motion characteristics, namely, all the components rotating about the center of rotation. Using the derived dynamic model, a multiobjective optimization problem is formulated to optimize the structural and geometric parameters of the spherical parallel manipulator. The proposed approach is illustrated with the design optimization of an unlimited-roll spherical parallel manipulator with a main objective to minimize the mechanism mass in order to enhance both kinematic and dynamic performances.
Mechanism and Machine Theory, 2018
This paper revisits some fundamental issues in kinematic analysis of spherical parallel robotic manipulators (SPRMs), such as the orientation capacities of the mobile platform (MPF), and assembly modes determination. The orientation capacities are analyzed by using several types of workspaces: total orientation workspace, full-spin orientation workspace, and constant-spin orientation workspace. The adopted representation of the MPF orientation brings up-to-date the use of the spherical coordinate system, which we find more appropriate when Euler angle orientation parameters are used. This representation is applied to each limb, considered independent from the rest of the mechanism and having the mobile platform as end-effector. The 3D orientation space reached by each limb, which is called also vertex space, is represented as a 3D solid volume. Thereafter, the operational space of the SPRM is directly determined by the Boolean intersection of the previously obtained volumes. Moreover, by fixing the joint space variables, the domain reached by each limb in the operational space is a surface. The Boolean intersection of the obtained surfaces is nothing but the set of points corresponding to the solutions of the forward kinematic problem. These operations are implemented in CAD software and the proposed approaches have been validated successfully by using several examples of application for both workspace determination and representation and FKP resolution.
A family of spherical parallel manipulators with two legs
Mechanism and Machine Theory, 2008
In this work a family of spherical parallel manipulators with a simple architecture is introduced. The primary feature of this family is to have a compact asymmetrical topology consisting of two legs and one spherical joint. This kind of topology is in agreement with the parallel manipulator definition of IFToMM-a parallel manipulator ''that controls the motion of its end effector by means of at least two kinematic chains going from the end effector towards the frame.'' Analytical expressions for the forward position, velocity and acceleration of the parallel manipulators have been obtained and solved for an exemplary manipulator. The forward displacement analysis, free of estrange or undesirable solutions, gives four possible orientations for the moving platform, which only require less than a second to generate. Afterwards, the velocity and acceleration analyses are approached by means of the theory of screws. The numerical results from the analytical expressions are verified by comparing them to the results from a mechanical system simulation software as if a real parallel manipulator is being run to collect the position, velocity and acceleration data. Finally, the singularity analysis is approached in analytic form.
Robotica, 2008
In this paper, a novel spherical parallel manipulator and its isotropic design is introduced. This manipulator has good accuracy and relatively a larger workspace which is free of singularities. Utilizing spherical configuration the forward position problem is solved by equivalent angleaxis representation and Bezout's method which leads to a polynomial of degree 8. Two examples are given, one for isotropic and one for nonisotrpoic design. The first case results in eight real solutions, therefore, the polynomial being minimal. Using invariant form, we study acceleration analysis, conditions for singularity and find infinite isotropic structures. Accuracy and workspace analysis are also performed and are shown to have good global conditioning index and relatively large workspace. Using isotropic design and singularity requirements, we show the workspace of isotropic design is free of singularity.