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Position control of the mechanical structure with naturally limited stiffness is a common problem. Moreover, the system is usually exposed to random exciting by the external force effects and yet it is needed to hold the system in the desired position. Such an example in engineering practice can be the machine tool quill slim structure, which determines the machining accuracy and the machined surface quality. The limited structure stiffness can be overcome by suitable support structure solution. In principle, it is a matter of introducing the necessary force effect in the place where it is necessary to ensure the required position. A promising means how to apply control force to the flexible structure tip can be a thin cable structure with the force actuation and proper force control. The resulting system is characterized by increased stiffness achieved in a mechatronic manner. Therefore, the introduced concept is called mechatronic stiffness. The article describes selected mechanical arrangement of the mechatronic stiffness concept, its features, behaviour and control results. The proposed approach offers a solution for precise position control of the flexible structure. An experimental device was created in parallel with the simulation experiment and preliminary simulation results are obtained. The described concept is transferable to other flexible structures such as various manipulators.

Undesired vibration is a common issue when dealing with manufacturing machines, especially when dealing with thin structures. To decrease the external disturbance sensitivity of such systems, represented for example by machine tool quill, the auxiliary cable structure is attached to the system. The auxiliary cable structure increases system damping and decreases undesired structure vibrations by the passive or active way, depending on the deployment and purpose. In this article, cables are attached to the end-effector to suppress undesired vibrations and related experimental stand is prepared. Experimental stand parameters are identified using least square method. The control strategy using pole placement is presented and its suitability is verified using external disturbance force. The frequency analysis shows the promising behaviour of controlled cable structure attached to the original system as well as the experimental results.

The paper deals with the creation and implementation of a methodology for optimizing the parameters of cascade control of the machine tool axis drives. The first part presents the identification of a dynamic model of the axis based on experimental data from measuring the axis dynamics. The second part describes the controller model, selection of optimization objective functions, and optimization of constraint conditions. The optimization of controllers is tuned by simulation using identified state-space model. Subsequently, the optimization procedure is implemented on the identified model, and the found control parameters are used on a real machine tool linear axis with different loads. The implementation of the proposed complex procedure on a real horizontal machine tool proved the advantage of simultaneous tuning of all parameters using optimization methods. The strategy solves the problem of mutual interaction of all control law parameters disabling effective usability of gradual sequential tuning. The methodology was developed on a speed control loop, the tuning of which is usually the most difficult due to the close interaction with the dynamic properties of the machine mechanics. The whole procedure is also applicable to the position and current control loop.

The concept of wave-based control (WBC) has been around for about two decades. It is designed primarily for controlling the end-point motions of one-dimensional lumped mass flexible chains. The systems under consideration are, therefore, severely underactuated. Typical control objective for such systems is a point-to-point motion without unwanted residual oscillations. These oscillations, however, become troublesome especially for the lightly damped cases. The only way to attenuate them is to ‘shape’ the control input. For this WBC concept considers a set of hypothetical (forward and backward) motion waves, which combine to form the actual motions. This document critically investigates wonderful properties of WBC which are claimed over the years and presents a completely new mathematical and rigorous treatment of the method. We rectify several misconceptions, especially on the level of a priori knowledge which is required on the system dynamics. Second, the authors present a novel step-by-step procedure to design a WBC law which ultimately leads to a number of opportunities for future explorations. Finally, the necessary and sufficient conditions in system parameter space for the stability of WBC are rigorously elucidated for the first time in the literature to the best of our knowledge.

This work deals with the control of flexible structures as underactuated systems. The invariant control method performs the control of a flexible robot as a representative of an underactuated system with zero dynamics. The control input is separated into two parts. The arbitrary part of the control input is designed to control the directly actuated part of the dynamic system. The invariant part of the control is selected to steer the system zero dynamics in the desired way. The harmonic functions create the base for the invariant part of the control function. The residual vibration cancellation is the target of the presented invariant control strategy. The harmonic function frequencies are overtaken from the so-called natural motion, amplitudes are the results of the optimization process. The main target of this paper is to show the invariant control approach and its application to the system with flexible elements.

Pointing consists in orienting a line OP of a rigid body, with its point O fixed, P mobile. The operation can thus be achieved in two steps, one to provide P with the desired longitude on the sphere centered at O, of radius OP ¯ , the other to provide P with the desired latitude. While this operation is simpler than a full rigid-body rotation, its kinematics is not yet fully recorded in the literature. In fact, the kinematics of pointing cannot be considered as being included in the kinematics of spherical motion, because the latter is known to form a Lie group, while pointing operations do not. This paper is an effort to shed light on the kinematics of pointing by means of the visualization of the workspace of the mechanism used for its realization. In doing this, a strategy is proposed for the planning of pointing trajectories using a three-revolute spherical wrist. The contributions proposed by the authors thus target the workspace visualization and the path-planning of three-axis wrists when used for pointing operations.

The paper deals with the modeling and control of redundantly actuated parallel mechanisms. The redundant actuation means the redundant number of actuators, that is, more actuators than degrees of freedom of the mechanism. These machines bring the possibility of removing the backlash by the so-called antibacklash control. However, control of such a structure suffers from several new control problems like the danger of mutual fighting of the redundant actuators. This is especially problematic if the geometric imperfections appear. The presented solution is based on the usage of robust sliding mode control for uncertain dynamics. The paper explains classic approach of sliding mode control and its new modification based on the uniform usage of all actuators replaced by the fictitious auxiliary drives. The verification of the proposed algorithms is presented by two planar mechanisms with four actuators and three degrees of freedom. The first one is the fiber-driven mechanism, and the second one is the rigid 4RRR mechanism “Crosshead.”

SUMMARYThe paper deals with the development and application of a new adaptive calibration method that extends the geometrical calibration of mechanisms from calibration of only dimensions and kinematical joint positions into the calibration of kinematic joint shape imperfections. Originally unknown nonlinear properties of the kinematical pairs are adaptively included into the kinematical models that are used during the calibration calculation. The method uses description by local linear models and validity functions in order to identify and describe nonlinear properties of the kinematical pairs. During each calibration step, various models with growing complexity are considered before the best model variant is selected to improve calibration results. The method is mainly devoted to the structures with many loops like parallel and fiber-driven parallel mechanisms. The method is applied to parallel mechanism Sliding Star and parallel fiber-driven mechanism Quadrosphere.

Typically single-mass absorbers combat a single excitation frequency at a time. In this paper we explore a novel control scheme to handle multiple and time-varying frequencies, but again using a single-mass absorber. The key scientific contribution is in the new way the spectral sensitivity is induced to the absorber substructure at multiple frequencies. This tuning process is achieved using a novel extension to the conventional Delayed Resonator (DR) concept with several delays. We show that the method can track all frequencies in real time. Therefore the new conception dramatically expands the traditional fixed-frequency absorption operations, for instance Dual Frequency Fixed Delayed Resonator (DFFDR). On-line deployment starts with a selection of a base delay in the feedback control on a given passive absorber. Necessary feedback gains for proper tuning are evaluated and control decision is made in real time. The stability repercussions of this control law, however, need to be assessed in advance. For this we use a recent characteristic root approximation method, QPmR (Quasi-Polynomial Mapping Based Root finding). These assessments create some restrictions for tunable frequency ranges with guaranteed stability. Such limitations, as well as the practical complexities of the new tuning method are also discussed over an example case study.

The paper deals with the new approach of the kinematical synthesis based on the reformulation of the synthesis computations as a time evolution of the nonlinear dynamical dissipative system. The synthesis/optimization objective functions are constructed based on the network of mechanism positions within the desired workspace. All synthesized parameters of the mechanism are in the associated dynamical system introduced as time-varying and generally different in the different positions. The important points and/or important lines are equipped with the fictitious masses and/or moments of inertia, the differences of parameters generates the correction forces, and the gradual dissipation of the kinetic energy is ensured by dampers connected between the inertial frame and the masses (sky-hook concept). The correction forces couple the auxiliary dynamical subsystems created in different positions. The nonzero correction forces are generated as long as the values of the corresponding parameters across the positions differ. The synthesis process is realized as the time evolution of such a system. The main advantage of the method for solving mechanisms’ synthesis is that it uses the unassembled configurations of the mechanisms by evolution of the time varying parameters. The mechanism search thus smoothly goes through the space of system parameters without inefficient penalization of the unassembled configurations. This space provides possible valuable solution of the more robust kinematical synthesis of the mechanisms. The applications for the different types of synthesis tasks and optimization of different objective functions like the optimization of the mechanism transmission or the multi-objective optimization of dexterity measure and the built-up space are straightforward, as described within the presented examples. The efficiency of the method can be improved using several re-activations of the evolution process.

This paper deals with the solution of three key problems for enabling the consideration of the massive parallelization for multibody dynamics. Instead of classical joints, the flexible joints with appropriate stiffness and damping are introduced in the multibody system, which enables to derive completely decoupled equations of motion and as a consequence to simulate them using massive parallel computing. Such formulation causes the uprise of high frequencies in the solution. Therefore, the heterogeneous multiscale method is used for numerical integration. However, three key problems had to be solved prior to such multibody simulation could be considered for further development. The problems are: the clear distinction of macro-model and micro-model in order to really reduce the eigenvalues of the integrated model, the completely decoupled procedure for estimation of reaction forces for each micro-integration restart, and the suitable choice of microintegration time length.

The paper deals with the research of the influence of design parameters on calibration of the machines. The calibrability is introduced as a mechanism property describing the sensitivity of calibrating dimension accuracy and end-effector positioning accuracy with respect to the accuracy of sensor measurements. The calibrability should be optimized in a very early stage of the design process. The optimization of calibrability leads to the minimization of the error transfer from sensors to end-effector and consequently to the improvement of the final accuracy of the machine operations. The calibrability should be used within the design process of a new parallel kinematical structures as a pendant of other traditional design criterions. The context of the new design criterion is discussed using the examples of parallel machines Trijoint 900H and Sliding Star. Finally the calibrability is used as a main design criterion of a spatial redundant parallel calibrating and measuring machine RedCaM.

The paper describes the extension of the composite rigid body formalism for the flexible multibody systems. The extension has been done in such a way that all advantages of the formalism with respect to the coordinates of large motion of rigid bodies are extended to the flexible degrees of freedom, e.g. the same recursive treatment of both coordinates and no appearance of O(n 3 ) computational complexity terms due to the flexibility. This extension has been derived for both open loop and closed loop systems of flexible bodies. The comparison of the computational complexity of this formalism with other known ap- proaches has shown that the described formalism of composite rigid body and the residual algorithm based on it are more efficient formalisms for small number of bodies in the chains and deformation modes than the usual recursive formalism of articulated body inertia.

The paper describes the multibody formalism based on natural coordinates and modified state space that is suitable for real-time applications. The complex multibody systems include closed loops and thus result into DAE equations. Their simulation then usually requires iterative stabilization. The described multibody formalism has two important properties making it suitable for real-time applications. Firstly, it provides the stable solution of DAE equations for multibody systems with kinematical loops without necessity of iterations. Secondly, it consists of system matrices with simple expressions (constant, linear or quadratic terms) for their elements and thus it is very suitable for massive parallelization. The resulting computational complexity is growing only linearly with the number of DOFs despite any occurrence of kinematical loops and it is about 5 times smaller than the recursive multibody formalisms.

The paper deals with the design and control of an example of redundantly actuated parallel kinematic structure that can be a machine tool. The principle of redundant actuation brings parallel kinematic structures which do not have singular positions in workspace and which has increased dynamic, stiffness and accuracy properties. There is proposed a parallel kinematic structure called Sliding Star that has promising dynamic and stiffness properties. The conceptual design-by-optimization of this structure is briefly described. The redundantly actuated parallel kinematics have control problem due to mutual fighting of redundant drives. There is described the solution of this problem. Based on the investigated redundantly actuated parallel kinematics there has been built a laboratory prototype. The experimental results from the control of this prototype are briefly presented.

The majority of engineering designs can be described as configuration design. The solution of configuration design is not only the satisfaction of constraints and requirements, but the solution requires the optimized variant. However, there are usually multiple objectives and corresponding design problem in a multiobjective one. Even for relatively small problems the solution space is large and the computational complexity can be very high with exponential growth. Another problem of configuration design is the usual nonlinear and non-monotonic character of engineering design. The efficient computation of multiobjective global optimisation is a powerful general way for solving the nonlinearity and non-monotonicity of design problems.

The paper deals with the formulation and thesolution of the global dynamic problem for multibody systemsgenerally described by redundant coordinates (DAE equations) andwith a redundant number of actuators.Within the dynamics of multibody systems two basic well-known problems have been investigated: the solution of direct dynamicsand the solution of inverse dynamics. Both of these problems enableus to solve in each time instant the relation between the motiondescribed by positions, velocities, accelerations and the actingforces. However, such solutions obtained in isolated timeinstants do not provide us with the global overview about thedynamic capabilities of a mechanical system, i.e. about theaccessible motion described by accessible positions, accessiblevelocities, accessible accelerations and the required (given)forces. Thus, besides the two basic dynamical problems there isa third one: the global dynamic problem.The formulation of the global dynamic problem, the generalmethods for its solution and the specific methods for itssolution for robots and manipulators are included.

This paper deals with the efficient extension of the recursive formalism (articulated body inertia) for flexible multibody systems. Present recursive formalisms for flexible multibody systems require the inversion of the mass matrix with the dimension equal to the number of flexible degrees of freedom of particular bodies. This is completely removed. The paper describes the derivation of equations of motion expressed in the local coordinate system attached to the body, then the discretization of these equations of motion based on component mode synthesis and FEM shape functions and, finally, two versions of the new recursive formalism.

Within the EC project Copernicus SADTS (Semi-Active Damping of Truck Suspensions and its Influence on Driver and Road Loads) a semi-active suspension for SKODA-LIAZ truck prototype is being developed. The objective is to decrease the dynamic road-tyre forces in order to reduce the road damage. It was necessary to find a suitable truck prototype, develop and verify a simulation model, propose different control concepts, and implement them on the truck prototype. This paper briefly describes the development stages of the project and the results finally achieved.