Coordination of Movements of Two-Handed 12-DOF Robot Manipulators at Their Joint Manipulation

The study focuses on a two-handed robot with twelve degrees of freedom, six for each arm, and gives an example of calculating generalized coordinates for the two-armed robot limbs at their joint manipulation. The initial data for obtaining generalized coordinates are represented by the location of the work object, which is a cube. When solving the problem, the last arm links reach the faces of the work object with a given orientation. To obtain generalized coordinates, we used a hierarchical approach, which is based on an algorithm for solving the inverse problem of kinematics, and developed a control flow chart. The values ??of generalized robot coordinates were obtained for each location of the object of work, taking into account the kinematic constraints in the joints of the robot actuator. Findings of research show that it is possible to obtain generalized coordinates for the coordinated movement of the robot actuators with tree-like kinematic scheme.

MATHEMATICAL MODEL OF THE DYNAMICS OF A SIX-MASS SYSTEM OF A PARALLEL STRUCTURE MANIPULATOR MECHANISM

The paper is devoted to the construction of a mathematical model of the dynamics of a parallel structure manipulator with three controlled degrees of freedom, based on the reduction of the kinetic energy of the manipulator to a quadratic form relative to three independent generalized coordinates, comparative results of mathematical modeling are presented.

STABILIZATION OF THE SPATIAL POSITION OF THE MANIPULATOR OF A PARALLEL-SEQUENTIAL STRUCTURE

A method for constructing terminal control based on the representation of control functions relative to time is considered. The parameters of the functions are determined from the condition of satisfying the boundary conditions at the ends of the trajectory of the generalized coordinates of the manipulator. On the basis of the obtained program movements, a control law with feedbacks is constructed.

Group interaction of robots with an arbitrary kinematic diagram of manipulators during synchronous execution of technological operations

The stabilization of the manipulated object near the position of static equilibrium under kinematic and force disturbances during cooperative transportation by two robots of arbitrary structure is considered. The dynamic balance of an object in grippers is described by the Mathieu equation. The controlled executive system of the coupled robot provides adjustment of the manipulation system with minimal potential energy in the grippers. A variant of the optimal control in terms of speed is considered when transferring the system to a position close to static equilibrium. Keywords: robot, group control, controlled generalized coordinates, continuity of connections, cooperative work. [email protected]

STUDY OF THE DYNAMICS OF THE EXOSKELETON ACTUATING UNIT

A person has more than 300 degrees of mobility, but it is practically impossible to recreate such a kinematic scheme. In this article, a kinematic scheme of the exoskeleton is proposed that is most necessary for human movement. A 3D model of the exoskeleton actuating unit with an electrohydraulic drive has been developed in the CAD system and the values of masses, coordinates of mass centers, inertia tensors of the links of the exoskeleton actuating unit have been calculated. A launch file has been developed in the MATLAB environment for modeling the dynamics of the exoskeleton actuating unit. The control laws in the degrees of mobility of the actuating unit of the exoskeleton are selected. As a result of the theoretical study, the ranges of changes in the generalized coordinates for the joints under study are determined. The dependences of the power and the moment in the joints 9, 10 on time are obtained. The conducted studies have shown that lifting the leg will require more energy and this makes it necessary to develop power plants, explore various types of drives and ways to control them energy-efficiently. The obtained data can serve in the development of a medical exoskeleton.

Dwelling on the Connection Between SO(3) and Rotation Matrices in Rigid Multibody Dynamics – Part 2: Comparison Against Formulations Using Euler Parameters or Euler Angles

We compare three solution approaches that use the index 3 set of differential algebraic equations (DAEs) to solve the constrained multibody dynamics problem through straight discretization via an implicit time integrator. The first approach is described in a companion paper and dwells on the connection between the orientation matrix and the SO(3) group. Its salient point is that the orientation matrix A is a problem unknown, directly computed without resorting to the use of other position-level generalized coordinates such as Euler angles or Euler parameters. The second approach employs Euler angles as part of the position-level generalized coordinates, and uses them to subsequently evaluate the orientation matrix A. The third approach replaces the Euler angles with Euler parameters (quaternions). The numerical integration method of choice in this contribution is first order implicit Euler. We report a similar number of iterations for convergence for all solution implementations (called rA, rε, and rp); we also observed an approximately twofold speedup of rA over rp and rε. The tests were carried out in conjunction with three models: simple pendulum, slider crank, and four-link mechanism. These simulation results were obtained using two Python simulation engines that were developed independently as part of this formulation comparison undertaking. The codes are available in a GitHub public repository and were developed to provide two different perspectives on the formulation performance issue. The improvements in simulation speed are traced back to a simpler form of the equations of motion and more concise Jacobians that enter the numerical solution. It remains to investigate whether these speed gains carry to higher order integration formulas, where the underlying Lie-group structure of SO(3) brings additional complexity in the rA solution.

Classical n-body system in geometrical and volume variables: I. Three-body case

We consider the classical three-body system with [Formula: see text] degrees of freedom [Formula: see text] at zero total angular momentum. The study is restricted to potentials [Formula: see text] that depend solely on relative (mutual) distances [Formula: see text] between bodies. Following the proposal by J. L. Lagrange, in the center-of-mass frame we introduce the relative distances (complemented by angles) as generalized coordinates and show that the kinetic energy does not depend on [Formula: see text], confirming results by Murnaghan (1936) at [Formula: see text] and van Kampen–Wintner (1937) at [Formula: see text], where it corresponds to a 3D solid body. Realizing [Formula: see text]-symmetry [Formula: see text], we introduce new variables [Formula: see text], which allows us to make the tensor of inertia nonsingular for binary collisions. In these variables the kinetic energy is a polynomial function in the [Formula: see text]-phase space. The three-body positions form a triangle (of interaction) and the kinetic energy is [Formula: see text]-permutationally invariant with respect to interchange of body positions and masses (as well as with respect to interchange of edges of the triangle and masses). For equal masses, we use lowest order symmetric polynomial invariants of [Formula: see text] to define new generalized coordinates, they are called the geometrical variables. Two of them of the lowest order (sum of squares of sides of triangle and square of the area) are called volume variables. It is shown that for potentials which depend on geometrical variables only (i) and those which depend on mass-dependent volume variables alone (ii), the Hamilton’s equations of motion can be considered as being relatively simple. We study three examples in some detail: (I) three-body Newton gravity in [Formula: see text], (II) three-body choreography in [Formula: see text] on the algebraic lemniscate by Fujiwara et al., where the problem becomes one-dimensional in the geometrical variables and (III) the (an)harmonic oscillator.

ENGINEERING METHOD FOR MODELING THE OUTER BALLISTICS OF ROTATIONAL AND PROGRESSIVE MOVEMENT DUMBBELLS

The work is devoted to the method of delivering a fire extinguishing agent into a distant fire zone. In a known method, a substance (for example, a fire extinguishing powder) is placed in a solid shell - a cylindrical container. After delivery to the location of the fire, the container should collapse and free up the substance that will be assisted on fire extinguishing. A pneumatic gun is used to deliver a cylindrical container. In the process of delivery, the cylinder should rotate around its axis to ensure the stability of the movement. At the same time, during the "shot", the difficulty of regulating the distribution of compressed air flows in the gun dulk to achieve the required speed of rotation of the cylinder is arisen. In a new delivery method, it is proposed to use a container consisting of two spherical containers connected by a rod (like dumbbells). Traditional motion modeling Dumbbells is based on the preparation and solution of the system of differential equations of Lagrange of the second kind. To do this, choose the functions of generalized coordinates and use Lagrangian to describe the rotational and progressive movement of dumbbells in the earth's field. This allows you to obtain approximate functional dependences, as well as dependencies of derivatives for each of the functions of generalized coordinates. As a result, you can depict charts of phase trajectories of the generalized coordinates. The dependence on time for the functions of generalized coordinates allow you to simulate the outer ballistics dumbbells - i.e. Create a computer animation of its rotational and progressive movement. In contrast to the traditional approach in this paper, an engineering method of geometric modeling of the external ballistics of the movement of dumbbells is proposed. Those. The method of modeling the rotational and progressive movement dumbbells, which is based on geometric representations. We assume that the auxiliary circle is rigidly fixed on the dumbbells, the center of which coincides with the center of mass dumbbells. Let the circle "quoted" along the ballistic trajectory of the Mass Dumbbell Center. Then the trajectories of the point mass of cargo dumbbells will give an approximate view of the rotational and progressive movement of dumbbells into spacious within the vertical plane.

Dynamic analysis of a belt transmission with the GMS friction model

The paper presents a certain method of analysing the dynamics of a belt transmission. A flat transmission model developed by us was presented. For the analysis, it assumed the transmission 5PK belt. A discrete belt model, being a system of rigid beams interconnected with flexible and shock-absorbing elements, was used. To account for the mutual influence between the belt and pulleys, the Kelvin–Voigt contact model was used. The GMS friction model was also implemented, which allows all basic known friction phenomena to be taken into account. For this purpose, the vector of generalized coordinates was expanded with additional sub-systems of coordinates modelling the flexible belt-pulley connection. Moreover, two additional cases of a sudden transmission start were presented: with values of driving and resistance torque not causing a significant slip in the transmission as well as values of torque that cause slip.