It has been a pleasure for me to arrange this Special Issue of Roboticaon Parallel Robots which provides 9 papers from authors from Asia, Oceania,North America and Europe; worldwide research on this topic is proof of thegrowing interest of both the scientific and the industrial areas of parallelmechanisms. I truly believe that the main reason for this enthusiasm is thatparallel mechanisms research extends from theoretical mathematics and kinematicsto applied robotics, and even beyond, creating new technologicalchallenges.

A method to determine the two parameter set of circular cylinders, whosesurfaces contain three given points, is presented in the context of an efficientalgorithm, based on the set of two parameter projections of the points ontoplanar sections, to compute radius and a point where the axes intersect theplane of the given points. The geometry of the surface of points, whose positionvectors represent cylinder radius, r, and axial orientation, isrevealed and described in terms of symmetry and singularity inherent in thetriangle with vertices on the given points. This strongly suggests that, givenone constraint on the axial orientation of the cylinder, there are up to sixcylinders of identical radius on the three given points. A bivariate function,in two of the three line direction Plücker coordinates, is derived to provethis. By specifying r and an axis direction, say, perpendicular to agiven direction, one obtains a sixth order univariate polynomial in one of theline coordinates which yields six axis directions. These ideas are needed in thedesign of parallel manipulators

In this paper we present a technique for designing planar parallelmanipulators with platforms capable of reaching any number of desired poses. Themanipulator consists of a platform connected to ground by RPR chains. The set ofpositions and orientations available to the end-effector of a general RPR chainis mapped into the space of planar quaternions to obtain a quadratic manifold.The coefficients of this constraint manifold are functions of thelocations of the base and platform R joints and the distance betweenthem. Evaluating the constraint manifold at each desired pose and defining thelimits on the extension of the P joint yields a set of equations.Solutions of these equations determine chains that contain the desired poses aspart of their workspaces. Parallel manipulators that can reach the prescribedworkspace are assembled from these chains. An example shows the determination ofthree RPR chains that form a manipulator able to reach a prescribedworkspace.

This paper presents a design methodology for parallel robots having tosatisfy a set of performance constraints. Some of these constraints are used tocompute a closed region in the parameters space (in which a point define anunique robot geometry) which define all the robot geometries fulfilling theseconstraints. Then a grid is created over this region and for each node of thisgrid the requirements, expressed in a high level language, are evaluated. Thenode leading to the robot best fulfilling the constraints is the designsolution.

Based on the singularity-consistent parameterization framework, weanalyze motion at direct kinematics singularities for a broad class of parallelmanipulators. It will be shown that taking into account the instantaneous motiondirection of the output link, additional insight can be gained for thepossibility to move through such singularities. We argue that direct kinematicssingularities should be analyzed over the dual space which, in turn, involvesthe state of the passive joints. We perform such an analysis based on theconditioning of the equation of motion. It is shown that, depending on theinstantaneous motion direction, at certain direct kinematics singularities it ispossible to obtain a consistent solution in terms of torque. This implies thatin combination with the continuity of the singularity-consistent inversekinematic solution, motion through such direct kinematics singularities isfeasible.

This paper presents the kinematics and dynamics of asix-degree-of-freedom platform-type parallel manipulator with six revolute legs,i.e. each leg consists of two links that are connected by a revolute joint.Moreover, each leg is connected, in turn, to the base and moving platforms bymeans of universal and spherical joints, respectively. We first introduce akinematic model for the manipulator under study. Then, this model is used toderive the kinematics relations of the manipulator at the displacement, velocityand acceleration levels. Based on the proposed model, we develop the dynamicsequations of the manipulator using the method of the natural orthogonalcomplement. The implementation of the model is illustrated by computersimulation and numerical results are presented for a sample trajectory in theCartesian space.

A calibration method for a Stewart platform has been developed as partof a project aimed at developing a calibration method for a Delta robot. TheDelta has 3 degrees of freedom (DOF) but is more complex than the Stewartplatform for calibration purposes because an extra link is inserted in eachkinematic chain between the base and the Nacelle member.

A new kinematic design of a parallel spherical wrist with actuatorredundancy is presented. A special feature of this parallel manipulator is thearrangement of co-axial actuators which allows unlimited rotation about any axisinside a cone-shaped workspace. A detailed kinematic analysis has shown thatactuator redundancy not only removes singularities but also increases workspacewhile improving dexterity. The structure optimization has been performed with aglobal dexterity criterion. Using a conditioning measure, a comparison with anon-redundant structure of the same type was performed and shows that asignificant improvement in dexterity has been obtained.

In this paper, we will present a new 6-DOF parallel robot using a set oftwo Delta structures. An effective method is proposed to establish explicitrelationships between the end effector co-ordinates and the active and passivejoint variables. A simulation of the 2-Delta robot on a C.A.D. Robotics systemwill also be presented. This simulation will allow us to validate the cohesionof our calculations, and to show the workspace depending on the mechanicallimits on passive joints variables. Finally, an approach is proposed to studythe influence of small clearances of the passive joint on the precision of theposition and rotation of the effector. This approach is based on a conceptsimilar to that of Yoshikawa's manipulability.

During the past few years, there has been an increasing demand in thefield of precision engineering for fine motion in multi-degrees of freedomsystems. These applications motivated the development of a new robotics fieldcalled microrobotics. In this paper, we review both the design guidelines formicrorobots and the advantages of using parallel robots in very high precisionapplications. Parallel micromanipulators using elastic joints as well asstructures manufactured in single solid and metallic bellows areintroduced.

A potential panel method is proposed to solve the collision-free pathplanning problem for a free-flying robot operating in an obstacle filled 3-Denvironment. The problem is solved in three steps: (1) transform the arbitraryshaped obstacles in the 3-D workspace into simple convex polyhedrons; (2)generate an artificial potential field using the 3-D panel method in the 3-Dworkspace; (3) generate a streamline from the starting position towards the goalposition in the artificial potential field. The computational complexity of thepertinent algorithms justify the efficiency of the approach and itsapplicability in real-time. Simulation results illustrate the potential of theproposed approach. The reported research is the outgrowth of the 2-D method,already published.

A task based approach to the issue of redundant robots starts from thepremise that there are obstacles that cannot be removed from the working areaand which therefore must be avoided. This statement produces the requirement fora device with a certain degree of mobility, and stresses the need to ensure thatthe aim is twofold: reach the goal and avoid obstacles. But avoiding obstaclesis not the same objective as keeping as far away from an obstacle as possible;the primary goal is still to reach the target. In fact humans use soft contactto reach targets that are at the periphery of their reach. This soft distributedcontact has the effect of smoothing the surface of the object and hence there isan element of only being interested in obstacle detail at the appropriate scaleto achieve the task.

This paper describes a new approach to collisionavoidance based on using a global path finding algorithm, in this case usingLaplacian potential fields, in conjunction with a simple local geometricallybased algorithm for avoiding obstacles and maximising the use of manoeuvringspace in a manner which is not limited by digital computation resolution issues.This extra technique is in some ways analogous to the human soft contactapproach.

Three examples are presented to illustrate the robustness ofthe algorithm. In order to be able to compare results with other techniques, anenvironment measurement scheme is defined which gives an indication of thedifficulty of the trajectory being followed.

In this paper, we propose an approach which ensures the dynamicstability of a biped robot called “BIPMAN”. It is based on the correction of thetrunk center of mass acceleration and on the distribution of the forces exertedby the limbs on the trunk. This latter is performed by means of a linearprogramming method (the simplex method). The retained criterion allows tooptimize force distribution as well as trunk roll and pitch angles. Weightingfactors are introduced into this criterion in order to define criteria adaptedto specific tasks. Modifying these factors is a solution to the task transitionproblem. Many simulation results are presented to demonstrate criteria andconstraints influences on dynamic stability. They lead us to introduce a newapproach called RTCA (Real Time Criteria andConstraints Adaptation). This relies on the analysis ofposition, velocity and acceleration vectors for criterion real time adaptationand on forces analysis for constraints real time adaptation. The RTCA approach is finally validated through simulations results for a specifictask.

Sensor based robotic systems are an important emerging technology. Whenrobots are working in unknown or partially known environments, they need rangesensors that will measure the Cartesian coordinates of surfaces of objects intheir environment. Like any sensor, range sensors must be calibrated. The rangesensors can be calibrated by comparing a measured surface shape to a knownsurface shape. The most simple surface is a plane and many physical objects haveplanar surfaces. Thus, an important problem in the calibration of range sensorsis to find the best (least squares) fit of a plane to a set of 3D points.

We have formulated a constrained optimization problem to determine the leastsquares fit of a hyperplane to uncertain data. The first order necessaryconditions require the solution of an eigenvalue problem. We have shown that thesolution satisfies the second order conditions (the Hessian matrix is positivedefinite). Thus, our solution satisfies the sufficient conditions for a localminimum. We have performed numerical experiments that demonstrate that oursolution is superior to alternative methods.