Vigen Arakelian

Complete shaking force and shaking moment balancing of linkages

In this Chapter, new methods for the full shaking force and shaking moment balancing of linkages are considered. In Sect. 4.1, a new solution for the full shaking force and shaking moment balancing of four-bar linkages is discussed, which allows the complete shaking force and shaking moment balancing of in-line four-bar linkages with constant input speed by adding a class-two Assur group, i.e. a group which does not add any supplementary degree of freedom into the mechanism. It should be noted that the balancing of the shaking moment without counter-rotations of three particular classes of four-bar linkages is known and it was mentioned in the overview (see Sect. 2.1). However, such a method cannot be extended to general four-bar linkages. In the mentioned Section, it is proposed to dynamically balance the in-line four-bar linkages by adding articulated dyads.

Optimal Force Generation in Parallel Manipulators for Passing through the Singular Positions

It is known that a parallel manipulator at a singular configuration can gain one or more degrees of freedom and become uncontrollable, that is, it might not reproduce a stable motion along a prescribed trajectory. However, it is proved experimentally that there is possible passing through the singular zones. This was simulated and shown through numerical examples and illustrated on several parallel structures. In this paper, we determine the optimal dynamic conditions generating a stable motion inside the singular zones. The obtained results show that the general condition for passing through a singularity can be defined as follows: the end-effector of the parallel manipulator can pass through the singular positions without perturbation of motion if the wrench applied on the end-effector by the legs and external efforts of the manipulator are orthogonal to the twist along the direction of the uncontrollable motion. This condition is obtained from the tion of the uncontrollable motion. This condition is obtained from the inverse dynamics and analytically demonstrated by the study of the Lagrangian of a general parallel manipulator. Numerical simulations are carried out using the software ADAMS and validated through experimental tests.

Design and Prototyping of a New Balancing Mechanism for Spatial Parallel Manipulators

This paper proposes a new solution to the problem of torque minimization of spatial parallel manipulators. The suggested approach involves connecting a secondary mechanical system to the initial structure, which generates a vertical force applied to the manipulator platform. Two versions of the added force are considered: constant and variable. The conditions for optimization are formulated by the minimization of the root-mean-square values of the input torques. The positioning errors of the unbalanced and balanced parallel manipulators are provided. It is shown that the elastic deformations of the manipulator structure, which are due to the payload, change the altitude and the inclination of the platform. A significant reduction of these errors is achieved by using the balancing mechanism. The efficiency of the suggested solution is illustrated by numerical simulations and experimental verifications. The prototype of the suggested balancing mechanism for the Delta robot is also presented.

Self-Motions of General 3-RPR Planar Parallel Robots

We study the kinematic geometry of general 3-RPR planar parallel robots with actuated base joints. These robots, while largely overlooked, have simple direct kinematics and large singularity-free workspace. Furthermore, their kinematic geometry is the same as that of a newly developed parallel robot with SCARA-type motions. Starting from the direct and inverse kinematic model, the expressions for the singularity loci of 3-RPR planar parallel robots are determined. Then, the global behavior at all singularities is geometrically described by studying the degeneracy of the direct kinematic model. Special cases of self-motions are then examined and the degree of freedom gained in such special configurations is kinematically interpreted. Finally, a practical example is discussed and experimental validations performed on an actual robot prototype are presented.

Complete shaking force and shaking moment balancing of planar parallel manipulators with prismatic pairs

Abstract This article deals with the complete shaking force and shaking moment balancing of planar parallel manipulators with prismatic pairs. The cancellation of dynamic loads transmitted to the ground is a challenge for these types of manipulators. It is obvious that the classical methods based on the optimal redistribution of movable masses and additional counter-rotations can be used to cancel shaking force and shaking moment. However, balancing of parallel manipulators with prismatic pairs is attained via a considerably complicated design. This article shows that it is possible to balance planar parallel mechanisms by using Scott—Russell mechanisms. Such an approach enables counter-rotations to be divided by 2. Numerical simulations carried out using ADAMS software validate the obtained results and illustrate that the suggested balancing enables to create a parallel manipulator transmitting no inertial load to its base.

Gravity compensation in robotics

The actuator power required to resist joint torque caused by the weight of robot links can be a significant problem. Gravity compensation is a well-known technique in robot design to achieve equilibrium throughout the range of motion and as a result to reduce the loads on the actuator. Therefore, it is desirable and commonly implemented in many situations. Various design concepts for gravity compensation are available in the literature. This paper proposes an overview of gravity compensation methods applied in robotics. The examined properties of the gravity compensation are disclosed and illustrated via kinematic schemes. In order to classify the considered balancing schemes three principal groups are distinguished due to the nature of the compensation force: counterweight, spring or active force developed by an auxiliary actuator. Then, each group is reviewed through sub-groups organized via structural features of balancing schemes. The author believes that such an arrangement of gravity compensation methods allows one to carry out a systematized analysis and provides a comprehensive view on the problem.

On the Dynamic Properties of Flexible Parallel Manipulators in the Presence of Type 2 Singularities

In the present paper, we expand information about the conditions for passing through Type 2 singular configurations of a parallel manipulator. It is shown that any parallel manipulator can cross the singular configurations via an optimal control permitting the favorable force distribution, i.e., the wrench applied on the end-effector by the legs and external efforts must be reciprocal to the twist along with the direction of the uncontrollable motion. The previous studies have proposed the optimal control conditions for the manipulators with rigid links and flexible actuated joints. The different polynomial laws have been obtained and validated for each examined case. The present study considers the conditions for passing through Type 2 singular configurations for the parallel manipulators with flexible links. By computing the inverse dynamic model of a general flexible parallel robot, the necessary conditions for passing through Type 2 singular configurations are deduced. The suggested approach is illustrated by a 5R parallel manipulator with flexible elements and joints. It is shown that a 16th order polynomial law is necessary for the optimal force generation. The obtained results are validated by numerical simulations carried out using the software ADAMS.

Solution Regions in the Parameter Space of a 3-RRR Decoupled Robot for a Prescribed Workspace

This paper proposes a new design method to determine the feasible set of parameters of translational or position/orientation decoupled parallel robots for a prescribed singularity-free workspace of regular shape. The suggested method uses Groebner bases to define the singularities and the cylindrical algebraic decomposition to characterize the set of parameters. It makes it possible to generate all the robot designs. A 3-RRR decoupled robot is used to validate the proposed design method.

Complete shaking force and shaking moment balancing of the position-orientation decoupled PAMINSA manipulator

This paper deals with the complete shaking force and shaking moment balancing of the position-orientation decoupled PAMINSA manipulator. The dynamic reaction forces on the manipulators base are eliminated by making the total mass center of the moving links stationary. The reaction moments on the frame are eliminated by optimal control of the end-effector, which rotates with prescribed velocity. The numerical simulations carried out using ADAMS software demonstrate that the balanced manipulators transmit no inertia loads to their bases.

Shaking Forces Minimization of High-Speed Robots via an Optimal Motion Planning

This paper deals with the problem of shaking force balancing of high-speed robots based on a new optimal trajectory planning approach. The aim of the new approach is the optimal path planning of the robot links centre of masses, which allows a considerable reduction of the variable inertia forces transmitted to the robot frame. The efficiency of the suggested method is illustrated by a numerical simulation of a planar two links 2R serial robot, in which reductions in the shaking force of 63 % and in input torque of 84 % are achieved.