Elasto-dynamic analysis of a novel 2-DoF rotational parallel mechanism with an articulated travelling platform

This paper carries out the elasto-dynamic analysis of a novel 2 degrees-of-freedom (DoF) rotational parallel mechanism (RPM) with an articulated travelling platform by means of kineto-elasto dynamic method. The architecture of the proposed 2-DoF RPM is firstly described, and then its kinematic analysis is carried out by closed-loop vector method. On the basis of finite element analysis, the elasto-dynamic models of movable components are established before assembling to formulate the elasto-dynamic equations of the whole mechanism in the light of deformation compatibility conditions. The free vibration equation is then achieved to evaluate the natural frequency of the novel 2-DoF RPM. Finally, an example is illustrated and the results are verified by finite element software. It shows that the relatively high natural frequencies and good dynamic performance make the novel 2-DoF RPM a promising solution for pose-adjusting module of 5-DoF machine centre.     

A novel 3D parallel mechanism for the passive motion simulation of the patella-femur-tibia complex

Parallel mechanisms have been exploited for the kinematic modelling of the passive motion, i.e. the motion under virtually unloaded conditions, of the patella-femur-tibia human joint. In particular, a new mechanism is devised in this paper: a 3D model of the patella-femur relative motion is presented which, combined with a previous simplified model of the femur-tibia relative motion, provides a suitable tool for the design of knee prostheses. Although less accurate than a previously presented model of the patella-femur-tibia joint, the new mechanism still replicates passive knee motion quite well and is simpler from a mechanical point of view. Experimental results validate the efficiency of the proposed model.     

Proper motion of a vertically parallel two-wheeler

Leningrad University. Translated from Prikladnaya Mekhanika, Vol. 26, No. 7, pp. 84–89, July, 1990.     

The evolution of small rotational perturbations to a uniform rotation of a viscoelastic fluid contained between parallel plates

The transfer mechanism of momentum from the boundaries into the interior of a viscoelastic fluid is examined in the case when the boundary consists of two parallel plates.Special emphasis is given to the case of a Maxwellian fluid. It is seen that an increase in the azimuthal angular velocity at the boundaries progresses into the interior of the liquid in the form of a velocity discontinuity wave. Simultaneously, an axial circulatory flow pumps liquid from the low rotation region near the middle plane into the high rotation region near the boundaries. Detailed calculations are given for the intial stage of evolution.     

On the exponential stability of the permanent rotational motion of a gyrostat

This paper is devoted to the study of the problem of exponential asymptotic stability of the rotational motion of a gyrostat using servo-control moments which are applied to the internal rotors. The servo-control moments which impose the rotational motion are obtained. The stabilizing servo-control moments are obtained from the conditions to ensure exponential asymptotic stability of the desired motion. Estimations of the phase coordinations as exponential functions are presented. The method based on a choice of the structural form of the servo-control moments such that the equations of motion reduce to a system of differential equations with exponential asymptotic stability of an special solution.     

Approximate analytical solutions for oscillatory and rotational motion of a parametric pendulum

In this paper, the authors have studied dynamic responses of a parametric pendulum by means of analytical methods. The fundamental resonance structure was determined by looking at the undamped case. The two typical responses, oscillations and rotations, were investigated by applying perturbation methods. The primary resonance boundaries for oscillations and pure rotations were computed, and the approximate analytical solutions for small oscillations and period-one rotations were obtained. The solution for the rotations has been derived for the first time. Comparisons between the analytical and numerical results show good agreements.     

Impulsive motion of a non-Newtonian fluid between two oscillating parallel plates

An exact solution for the flow of an incompressible viscoelastic fluid between two infinitely extended parallel plates, due to the harmonic oscillations of the upper plate and the impulsively started harmonic oscillations of the lower plate from rest, in the respective planes of the plates, has been obtained. The momentum transfer towards the central region and the skin friction of the lower plate are found to be greater for the viscoelastic fluid than that for viscous fluid. The effect of out-of-phase oscillations of the plates with different amplitudes on the flow characteristics has also been investigated.     

Boundary layer development on a continuous moving surface with a parallel free stream due to impulsive motion

The development of the momentum and thermal boundary layers over a semi-infinite flat plate has been studied when the external stream as well as the plate are impulsively moved with constant velocities. At the same time the temperature of the wall is suddenly raised from T_∞, the temperature of the surrounding fluid, toT _w and maintained at this temperature. The problem has been formulated in a new system of scaled coordinates such that fort?=0 it reduces to Rayleigh type of equation and fort? → ∞ it reduces to Blasius or Sakiadis type of equation. A new scale of time has been used which reduces the region of integration from an infinite region to a finite region which reduces the computational time considerably. The governing singular parabolic partial differential equations have been solved numerically using an implicit finite difference scheme. For some particular cases, analytical solutions have been obtained. The results show that there is a smooth transition from Rayleigh solution to Blasius or Sakiadis solution as the dimensionless timeξ increases from zero to one. The shear stress at the wall is negative for the friction parameterλ<0.5, positive forλ>0.5 and zero forλ=0.5. The zero shear stress at the wall does not imply separation but corresponds to the parallel flow. The surface heat transfer is strongly dependent on the Prandtl numberPr and increases with it. Also forPr<Pr ₀, the surface heat transfer is enhanced as the friction parameterλ increases, but forPr>Pr ₀ it get reduced.     

Stability of unsteady rotational motion of a plane layer of ideal fluid with free boundaries

The exact solution of the equations of an ideal incompressible fluid describing the unsteady rotational motion of a plane layer with free boundaries is obtained. For constant vorticity the stability problem is studied in the linear approximation. The asymptotic behavior of the free boundaries of the layer as t is calculated. It is shown that the vorticity of the basic motion stabilizes the boundaries of the layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 15–21, March–April, 1986.     

Calibration of encoder indexing of a redundantly actuated parallel mechanism to eliminate contradicting control forces

This paper presents the kinematic calibration of a two degree-of-freedom redundantly actuated parallel mechanism (RAPM), with the aim of eliminating contradicting control forces (CCF). The kinematic errors in the RAPM induce CCFs, especially in the case of decentralized individual position control, which is the standard control method used in industrial applications. The encoder indexing errors of the actuated joints are known to be of strong influence on the CCFs. Therefore, it is believed that the CCFs will be eliminated if the encoder indexing errors are corrected. We proved this through experiments. We performed the calibration using a projection technique, wherein we projected tracking error terms onto orthogonal complementary terms of the constraint Jacobian between the independent joints and actuated joints. Using this projection technique, the effect of tracking error terms from the joint stiffness and external force is eliminated. During the calibration process, the tracking errors in the actuated joints are measured. Using these errors, we derived the optimal values of the encoder indexing error by minimizing the objective function. We verified the calibration result by comparing the CCFs measured before calibration with those measured after calibration, for the case of individual PID position control. Our results confirmed that the calibration procedure of encoder indexing errors successfully reduces the average norm value of CCFs from 366 N to 13 N.     

Kinematic modeling and dexterity evaluation of a PS-RRS-2RUS parallel manipulator used for controllable pitch propeller

This article investigates the kinematic modeling and dexterity evaluation of a PS-RRS-2RUS parallel manipulator. The design concept and mobility analysis of the manipulator are first addressed utilizing the screw theory. Second, the decoupled and closed-form kinematic solutions with multiple configurations are solved through vector method. Then, the analytical expressions for the velocity relationships are derived into a closed-form Jacobian matrix, which is then used to distinguish the singular postures. Finally, the workspace with fixed orientation is calculated and its dexterity is evaluated. The numerical simulations and validation are conducted in a case study.     

A method to carry out shape optimization with a large number of design variables

A new method for shape optimization with relatively large number of design variables is proposed. It is well known that gradient‐based methods converge to a local optimum. As a result, utilization of a richer design space does not necessarily lead to a better design. This is demonstrated via the design of an airfoil for maximum lift for Re = 1000 and α = 4° flow. The airfoil is represented by fourth‐order non‐uniform rational B‐splines, and the control points are used as design variables. Starting with a NACA0012 airfoil, it is found that the optimal airfoil obtained with 13 control points has far superior aerodynamic performance than the ones obtained with 39 and 61 control points. For effective utilization of a richer design space, it is proposed that the number of design variables be increased gradually. The method is demonstrated by designing high lift airfoils for Re = 1000 and 1 × 10⁴. The objective function is the maximization of the time‐averaged lift coefficient for α = 4°. The optimization cycle with 27 control points is initiated with the optimal airfoil obtained with 13 control points. The process is continued with gradual increase in the number of design variables. Beyond a certain number of control points, the optimization leads to a spontaneous appearance of corrugations on the upper surface of the airfoil. The corrugations are responsible for the generation of small vortices that add to the suction on the upper surface of the airfoil and lead to enhanced lift. A stabilized finite element method is used to solve the unsteady flow and adjoint equations. Copyright © 2012 John Wiley & Sons, Ltd.     

Disturbance compensation of a dual-arm underwater robot via redundant parallel mechanism theory

Disturbance compensation is one of the major issues for underwater robots to hover as a mobile platform and to manipulate an object in an underwater environment. This paper presents a new strategy of disturbance compensation for a mobile dual-arm underwater robot using internal torques derived from redundant parallel mechanism theory. A model of the robot was analyzed by redundant serial and parallel mechanisms at the same time. The joint torque to operate the robot is obtained from a redundant serial mechanism model with null-space projection due to redundancy. The joint torque derived from the redundant parallel kinematic model is calculated to perfectly compensate for disturbances to the mobile platform and is included in the solution of the joint torque based on the serial redundant model. The resultant joint torque can generate force on the end-effector for required tasks and forces for disturbance compensation simultaneously . A simulation shows the performance of this disturbance compensation strategy. The joint torque based on the algorithm generates the desired task force and the disturbance compensation force together, and a little additional joint torque can generate a large internal force effectively due to the characteristics of a redundant parallel mechanism. The proposed method is more effective than compensation methods using thrusting force on the mobile platform.     

Three-dimensional instability of two counter-rotating vortices in a rectangular cavity driven by parallel wall motion

The linear stability of two counter-rotating vortices driven by the parallel motion of two facing walls in a rectangular cavity is investigated by a finite volume method. Critical Reynolds and wave numbers are calculated for aspect ratios ranging from 0.1 to 5. This range is sufficient to find the asymptotic behavior of the critical parameters when the aspect ratio tends to zero and infinity, respectively. The critical curve is smooth for all aspect ratios and, hence, the character of the instability changes continuously. When the moving walls are far apart the mechanism is centrifugal, as in the classical lid-driven cavity. For aspect ratios near unity a combined mechanism, also involving strain near the vortex cores, leads to the instability which tends to asymmetrically displace the vortex cores, very similar to the cooperative short-wave instability of a free counter-rotating vortex pair. In the limit when plane Poiseuille flow is approached in the bulk, the three-dimensional perturbations are strongly localized near both downstream ends of the moving walls.     

A study on laminar motion of a viscous incompressible fluid between two parallel eccentric cylinders

The flow of incompressible viscous fluid between two eccentric cylinders under the action of a difference between the pressures imposed at the ends of the cylinders is analyzed. Using bipolar coordinates, the resulting boundary value problem is solved analytically, and the average flux velocity is calculated for various values of the geometric parameters of the problem.     

Inverse dynamics of a 3-PRC parallel kinematic machine

Recursive matrix relations for kinematics and dynamics analysis of a three-prismatic-revolute-cylindrical (3-PRC) parallel kinematic machine (PKM) are performed in this paper. Knowing the translational motion of the platform, we develop first the inverse kinematical problem and determine the positions, velocities and accelerations of the robot’s elements. Further, the inverse dynamic problem is solved using an approach based on the principle of virtual work and the results in the framework of the Lagrange equations with their multipliers can be verified. Finally, compact matrix equations and graphs of simulation for input force and power of each of three actuators are obtained. The investigation of the dynamics of this parallel mechanism is made mainly to solve successfully the control of the motion of such robotic system.