Energy minimization for 3-RRR fully planar parallel manipulator using particle swarm optimization

An investigation on stiffness of a 3-PSP spatial parallel mechanism with flexible moving platform using invariant form

Stiffness and mass optimization of parallel kinematic machine

Although stiffness analyses of specific parallelogram-type parallel manipulators (PTPMs) have been presented by several researchers, an algebraic expression is still needed to obtain the stiffness of a general PTPM. To address this issue, this paper uses a strain energy method considering the compliances of the mobile platform, the limb and the actuator of a PTPM. In this method, the deformation of the mobile platform, which has typically been ignored by many researchers, is integrated in the total deformation of the PTPM. After comparison with a FEA method, it is found that the proposed algebraic method is a comparable alternative to the FEA method to be used in the pre-design stage. Additionally, a new stiffness index is proposed to evaluate the stiffness property. Compared with other stiffness indices, the new index uses virtual work to unify the units of translation and orientation and relates the index value to the direction of the wrench experienced by a parallel manipulator in a task. With this index, the resistance of a PTPM to deformation under a given wrench can be measured easily. Stiffness analysis of a general PTPM using an algebraic method.Result comparison between the proposed method and a finite element analysis method.A new stiffness index relating the stiffness property to the wrench experienced in a task.

Stiffness analysis of parallelogram-type parallel manipulators using a strain energy method

Adaptive fuzzy inverse trajectory tracking control of underactuated underwater vehicle with uncertainties

This paper investigates the problems of kinematics, Jacobian, singularity and workspace analysis of a spatial type of 3-PSP parallel manipulator. First, structure and motion variables of the robot are addressed. Two operational modes, non-pure translational and coupled mixed-type are considered. Two inverse kinematics solutions, an analytical and a numerical, for the two operational modes are presented. The direct kinematics of the robot is also solved utilizing a new geometrical approach. It is shown, unlike most parallel robots, the direct kinematics problem of this robot has a unique solution. Next, analytical expressions for the velocity and acceleration relations are derived in invariant form. Auxiliary vectors are introduced to eliminate passive velocity and acceleration vectors. The three types of conventional singularities are analyzed. The notion of non-pure rotational and non-pure translational Jacobian matrices is introduced. The non-pure rotational and non-pure translational Jacobian matrices are combined to form the Jacobian of constraint matrix which is then used to obtain the constraint singularity. Finally, two methods, a discretization method and one based on direct kinematics are presented and robot non-pure translation and coupled mixed-type reachable workspaces are obtained. The influence of tool length on workspace is also studied.

/pdf/position-jacobian-and-workspace-analysis-of-a-3-psp-spatial-36mjndvy6e.pdf

Position, Jacobian and workspace analysis of a 3-PSP spatial parallel manipulator

This paper presents an improved general dynamic formulation, inverse and direct dynamics, of 6-UPS Gough–Stewart parallel robot based on the virtual work method. The new formulation offers a reduction in the computational time and improves accuracy of the dynamics equations. This method allows elimination of constraint forces/moments at the passive joints from equations of motion. Since, the dynamic formulations are derived in joint space, the concept of direct link Jacobian matrices are employed to obtain all rigid bodies’ twists. The direct link Jacobian matrices convert the twist of the rigid bodies to actuated joints velocities. Moreover, more accurate formulation is obtained by considering the angular velocity and acceleration vectors of the robot’s legs. In the process of solving the direct dynamics problem, a modified hybrid strategy is employed to obtain the near-exact solution for the direct kinematics problem (DKP). The modified hybrid strategy combines the artificial neural network and the third-order Newton–Raphson method. This strategy satisfies both goals to find the nearest exact solution and reduces execution time for the DKP. Next, two numerical examples are presented and the results are verified using a commercial dynamics modeling software. Finally, for comparison, Euler–Lagrange formulation is also obtained. Results indicates that the proposed dynamics formulation offers a significant improvement in both accuracy and execution time.

/pdf/improved-general-solution-for-the-dynamic-modeling-of-gough-2aob4oe6ya.pdf

Improved general solution for the dynamic modeling of Gough–Stewart platform based on principle of virtual work

http://profdoc.um.ac.ir/articles/a/1033750.pdf

An interval-valued fuzzy controller for complex dynamical systems with application to a 3-PSP parallel robot

In this paper, structural stiffness analysis of a new 3-axis asymmetric planar parallel manipulator, a 2 P RR–P P R structural kinematic chain, is investigated. The manipulator is proposed as a tool holder for a 5-axis hybrid computer numerical control (CNC) machine. First, the structure of the robot is introduced and inverse kinematics solution is presented. Secondly, stiffness matrix of the robot is determined using a continuous method based on Castigliano’s theorem and calculation of strain energy of the robot components. This method removes the need for commonly used simplifying assumptions and, therefore, results in good accuracy. For this purpose, force and strain energy for each segment of the robot are analyzed. Finally, to verify the analytical results, commercial FEM software is used to simulate the physical structure of the manipulator. A numerical example is presented which confirms the correctness of the analytical formulations.

Amir Rezaei

Papers

An investigation on stiffness of a 3-PSP spatial parallel mechanism with flexible moving platform using invariant form

Position, Jacobian and workspace analysis of a 3-PSP spatial parallel manipulator

Improved general solution for the dynamic modeling of Gough–Stewart platform based on principle of virtual work

An interval-valued fuzzy controller for complex dynamical systems with application to a 3-PSP parallel robot

Position and stiffness analysis of a new asymmetric 2PRR–PPR parallel CNC machine