This paper presents the further developments and preliminary results of a large 3D printing machine based on a 3 d.o.f cable-driven parallel robot (CDPR) that is used for an artistic exhibition. The printing material is a powder constituted of glass micro-beads that is deposited on a fixed trajectory so that the resulting structure collapses with time. A first exhibition has been held during the summer of 2019 and another one was scheduled to take place during ICRA 2020, that was canceled because of the Covid. The current exhibition has started on 07/09/2022 and will end on 10/14/2019. We describe in this paper the improvements of the current prototype, both on hardware and software, compared to the 2019 and 2020 versions. Between 7/9/2022 and 16/10/2022 the CDPR has run for 126 hours and has traveled on a total distance of 9km. During the period 142 layers have been deposited, representing a mass of 2.56 tons of glass powder.

Sagging cable-driven parallel robots (CDPRs) are often modeled by using the Irvine's model. We will show that their configurations may be unstable, and moreover, that assessing the stability of the robot with the Irvine's model cannot be done by checking the spectrum of a stiffness matrix associated with the platform motions. In this article, we show that the static configurations of the sagging CDPRs are local extrema of the functional describing the robot potential energy. For assessing the stability, it is then necessary to check two conditions: The Legendre–Clebsch and the Jacobi conditions, both well known in optimal control theory. We will also 1) prove that there is a link between some singularities of the CDPRs and the limits of stability and 2) show that singularities of the platform wrench system are not singularities of the geometric model of the sagging CDPRs, contrary to what happens in rigid-link parallel robotics. The stability prediction results are validated in simulation by cross-validating them by using a lumped model, for which the stability can be assessed by analyzing the spectrum of a reduced Hessian matrix of the potential energy.

This paper presents the development and results of a large 3 d.o.f cable-driven parallel robot (CDPR) that has been extensively used between June and August 2019 for an artistic exhibition. The purpose of the exhibition was to 3D print a wall of glass powder, which will slowly collapse after the deposit of each layer. Positioning control on the assigned trajectory was an issue because of the CDPR geometry imposed by the specific configuration of the exhibition place. We describe how this problem was solved using a combination of cable length estimation based on the winch rotation measured by encoder, together with 3 on-board lidars that were used to provide a measure of the robot position. To the best of our knowledge this is the first time that such method was used for controlling a large CDPR. This CDPR has run for 174 hours since 6/18/2019, averaging a run time of 4h15mn per day. The 3D printing of the wall started on 7/18/2019 and stops on 8/31/2019. During this period the robot was used for 32 days with an average of 2h18mn run-time per day. The robot has traveled on a total distance of 4757 meters, of which 3893 meters on the assigned trajectory. During the period 76 layers have been deposited, representing a mass of 1.5 tons of glass powder.

This paper addresses for the first time the singularity analysis of cable-driven parallel robot (CDPR) with sagging cables using the Irvine model. We present the mathematical framework of singularity analysis of CDPR using this cable model. We then show that, besides a cable model representation singularity, both the inverse and forward kinematics (IK and FK) have a singularity type, called parallel robot singularity, which correspond to the singularity of an equivalent parallel robot with rigid legs. We then show that both the IK and FK have also full singularities, that are not parallel robot singularity and are obtained when two of the IK or FK solution branches intersect. IK singularity will usually lie on the border of the CDPR workspace. We then exhibit an algorithm that allow one to prove that a singularity exist in the neighborhood of a given pose and to estimate its location with an arbitrary accuracy. Examples are provided for parallel robot, IK and FK singularities. However we have not been able to determine examples of combined singularity where both the IK and FK are singular (besides parallel robot singularity).

Positioning accuracy of cable-driven parallel robots is influenced by many factors such as geometry, actuator sensor accuracy and disturbances in the applied wrench. Another uncertainty source is the elasticity of the cables. While the influence of many factors may be decreased by calibration and/or sensor fusion, elasticity parameters are difficult to estimate and their effect on the positioning errors has yet to be determined. In this paper we consider a generic cable model that includes cable elasticity and the effect of cable weight and we propose a generic algorithm that allows one to safely calculate the minimum and maximum of the positioning error at a given pose when the elasticity parameters are constrained to lie within some given bounds. The algorithm is designed for being able to manage the effect of different uncertainties sources and we compare the influence of elasticity versus the effect of uncertainties in the cable lengths.

Solving the direct kinematics (DK) of cable-driven parallel robots (CDPR) based only on the cable length measurements is a demanding problem that is still not well mastered, especially for robots having sagging cables. A model-based approach may be used to solve this problem but the model parameters and measurements are uncertain, thereby leading to positioning inaccuracy. A possible way to improve the accuracy and speed up the solving is to add extra measurements. For that purpose a preliminary step is to determine what type of measurements are possible and then to estimate how accurate they are. For that purpose we have used a CDPR with 4 cables that has been instrumented with various types of extra measurements: cable tensions and orientations, platform orientation. Ground truth has been established and we have compared the data provided by the extra sensors with their real values. This work shows that cable tensions sensors and platform orientation sensors are not good candidates to be used for the DK while cable orientations may be obtained with a good accuracy both in static poses or during a quasi-static motion.

Although workspace is essential for the design and control of cable-driven parallel robots (CDPR) very few works have been devoted to this topic when sagging cables are considered, most probably because of the complexity of the cable model. In this paper we consider suspended CDPR with sagging cables that can support only a limited tension. We propose an algorithm to compute the border of horizontal cross-sections of the workspace for a given altitude and orientation of the platform. We show that singularities of the kinematics equations have to be taken into account for a proper determination of the border and that the workspace can be separated in several components according to the branch of the inverse kinematics on which the robot is evolving. We also compare the workspace obtained for ideal and sagging cables.

Direct kinematics (DK) of cable-driven parallel robots (CDPR) based only on cable lengths measurements is a complex issue even with ideal cables and consequently even harder for more realistic cable models such as sagging cable. A natural way to simplify the DK solving is to add sensors. We consider here sensors that give a partial or complete measurement of the cable direction at the anchor points and/or measure the orientation of the platform of CDPR with 2 or 3 cables and we assume that the measurements are exact. We provide a solving procedure and maximal number of DK solutions for an extensive combination of sensors for CDPR with sagging cables. We show that at least two measurements are necessary for the planar 2 cables case while six are necessary for the spatial 3 cables case. For spatial CDPR with n cables we prove that at least 2n additional sensors will be required to get a closed-form solution of the DK.

This paper addresses the simulation of the state of a discrete-time controlled cable-driven parallel robot (CDPR) with nondeformable or elastic cables over a given trajectory. Being given a CDPR, an arbitrary model for the coiling system and for the control strategy, we exhibit a simulation algorithm that allows one to determine, in a guaranteed way, the platform pose and the cable tensions at any time. We show that such a simulation may require a computing accuracy that imposes to use extended arithmetic and that discrete-time control may lead to drastic differences in the cable tensions as compared to usual continuous time simulation. Hence, the proposed simulation tool allows for a better estimation of the positioning accuracy together with safer estimation of the maximum of the cable tensions.

Workspace calculation for cable-driven parallel robot (CDPR) differs from the one for robots with rigid legs as the main limiting factor is the satisfaction of the mechanical equilibrium, being given a model for the cable behavior. We are considering here 6-dof CDPR with n ≥ 6 cables and are investigating the calculation of horizontal cross-sections of the workspace under the assumption that the orientation of the platform is constant. We show that for non deformable or elastic mass-less cables it is possible to calculate the border of the workspace under the constraints τmin≤ τ ≤ τmaxwhere τ is the cable tension and τmin, τmaxare constant thresholds. For sagging cables the calculation is much more complex: we present however a preliminary, computer intensive algorithm that allow to obtain an approximation of the cross-section as a set of boxes. We also emphasize that for CDPR the definition of the workspace as the set of poses that can be reached has to be considered stricto sensu and cannot be used for other purpose: for example the inclusion of a trajectory in the workspace is not a proof of the feasibility of this trajectory.

Solving the direct kinematics (DK) of parallel robots, i.e. finding all the possible poses of the platform for given input values, is most of the time a difficult problem. This is evidently true for cable-driven parallel robots (CDPR) that are more complex than classical parallel robot because of the unilateral nature of the cable actions but also if cable deformations are taken into account. Furthermore there are many different deformable cable models and developing a DK algorithm for each of them will be a tremendous task. Consequently using a numerical continuation scheme that starts from the DK solutions for non-deformable cables and then moves toward the solution for deformable cables appears to be an interesting approach. To use this scheme we have to assume that the cable model relies on physical parameters that have limit values for which the deformable cable acts like a non-deformable one. Under that assumption we are then able to derive a possible maximum of solutions for the DK, whatever is the cable model. We then apply this approach for a specific complex cable model, the catenary case, to show that this approach is computer efficient but requires to address difficult theoretical issues in order to obtain a solving algorithm that is guaranteed to determine all DK solutions.

We consider in this paper cable driven parallel robot (CDPR) with m catenary cables that present a significant deformation due to their elasticity and own mass and we address the kinematics of such a robot under the assumption of static state. We show that the inverse kinematics (IK) requires to solve a square system of equations if the robot has up to 6 cables and an underconstrained system if m > 6. We first show that usual methods for solving the IK of CDPR with other cable model cannot be used and we propose an algorithm that allows one to determine all possible solutions. We then address the forward kinematics (FK) that is known to be usually a difficult task for parallel robots. We show that solving the FK always amounts to solve a square system of equations and that the problem is even more complex than solving the FK of parallel robots with rigid legs as the system is non algebraic and has a larger number of equations. We then propose a generic algorithm for solving the FK for any number of cables. We illustrate the use of the IK and FK solver on a CDPR with 8 cables.

We consider in this paper cable driven parallel robot (CDPR) with m catenary cables that present a significant deformation due to their elasticity and own mass and we address the inverse kinematics (IK) of such a robot i.e. determining the lengths at rest of the cables for a given pose of the platform. We show that the IK requires to solve a square system of equations if the robot has up to 6 cables and an underconstrained system if the number of cables is larger than 6. In this paper we address the problem of finding all solutions of the IK when the number of cables is lower or equal to 6. We propose an algorithm that allows one to determine all possible solutions. for any number of cables. We illustrate the use of the IK solver on a CDPR with 6 cables and shows that the IK may have no solution even if the pose lie within the envelope of the base points or may have several solutions, in which case some cables may have a length at rest that is much larger than the distance between the anchor points of the cable.

This paper addresses the concept of cable configuration of cable-driven parallel robots (CDPR). At a given pose a cable configuration describes the state of cables, i.e. under tension or slack, and plays a major role for the cable tensions and the platform positioning errors. Being given a CDPR with non-elastic cables and a model for the coiling system we describe how the cable configuration can be determined in a guaranteed way for a desired trajectory of the platform. We show that if the CDPR has more than 6 cables it is extremely unlikely that more than 6 cables will be under tension simultaneously even under perfect conditions. It appears that on a trajectory the cable configuration exhibits multiple changes, leading to large variations in the cable tensions.

Our objective is to extend the assistance functionalities of the cable-driven parallel robot Marionet-Assist, designed principally for transfer operation, by allowing it to grasp usual objects (knives, box of medicines, phone, ···) by using visual servoing. Our crane robot has a configuration that provides three translational d.o.f., and a camera was added to its end-effector. In order to compute the translational velocity sent to the robot controller, the area and center of gravity in the image of the object to be grasped are used. Experimental results are presented. They show the robustness of our scheme with respect to modeling errors and an excellent positioning accuracy allowing grasping.

The kinematics of wire-driven parallel robot (WDPR) is one of the most challenging problem of modern kinematics. We investigate here the kinematics of two robots with 3 and 4 wires, in a crane configuration, having specific location of the anchor point on the platform. The 4-3-1 robot has 4 wires, three of them being connected at the same anchor point on the platform. We show that this robot has up to 4 solutions to the forward kinematics. The 3-2-1 robot has 3 wires, two of them being connected at the same point on the platform: we show that the forward kinematics solutions of this robot, that involves its static equilibrium, may be obtained by solving a polynomial of degree 64, leading to a maximum of 256 solutions to the FK. In both cases the proposed maximum number of solutions is much better than the one already known for robots of general structure having 3 or 4 wires. Numerical experiments let us conjecture that the 64th order polynomial will always factor out and that all roots will be obtained from a polynomial of degree 32, leading to at most 128 solutions and we have obtained examples with up to 10 solutions with positive tensions in the wires. We justify this study by experimentally showing that a 4-3-1 robot moving in its workspace may become a 3-2-1 robot as one wire become slack, numerical simulations showing that this will happen in more than 50% of the poses in the workspace (but the 4-3-1 has obviously a larger workspace than the 3-2-1, hence its interest).

This paper studies cable-driven parallel robots with less than six cables, in crane configuration. A geometrico-static model is provided, and the stability of static equilibrium is assessed within the framework of a constrained optimization problem. The method relies on ordinary linear-algebra routines, and it may be very simply applied to the most general architectures. Several examples are provided, concerning robots with a number of cables that range from 2 to 4.

We address the kinematics of the redundant N - 1 wire-driven parallel robot, i.e. a robot with N >; 3 wires connected at the same point on the platform. The redundancy allows one to increase the workspace size. But we show, both theoretically and experimentally that if the wires are not elastic, then the redundancy cannot be used to control the wire tensions. Indeed we show that whatever are the number of wires there will always be only at most 3 wires in tension, while the other N - 3 wires will be slack. We then show that if the wires are elastic, then the platform positioning will be very sensitive to stiffness identification and wire lengths control. Hence classical redundant control schemes are difficult to use for such robot and alternate use of the geometry of redundant wires have to be considered.

This paper studies under-constrained cable-driven parallel robots with three cables. A major challenge in the study of these manipulators is the intrinsic coupling between kinematics and statics, which must be tackled simultaneously. In this contribution, a general elimination procedure is provided that solves the direct geometrico-static problem, which consists in determining the platform posture and the cable tensions when the cable lengths are assigned. The problem is proven to have up to 156 complex solutions.

This paper deals with the wrench-feasible workspace (WFW) ofn-degree-of-freedom parallel robots driven bynor more thanncables. The WFW is the set of mobile platform poses for which the cables can balance any wrench of a given set of wrenches, such that the tension in each cable remains within a prescribed range. Requirements of nonnegative cable tensions, as well as maximum admissible tensions, are thus satisfied. The determination of the WFW is an important issue since its size and shape are highly dependent on the geometry of the robot and on the ranges of allowed cable tensions. The approach proposed in this paper is mainly based on interval analysis. Two sufficient conditions are presented, namely, a sufficient condition for a box of poses to be fully inside the WFW and a sufficient condition for a box of poses to be fully outside the WFW. These sufficient conditions are relevant since they can be tested, with the means to test them being discussed in the paper. Used within usual branch-and-prune algorithms, these tests enable WFW determinations in which full-dimensional sets of poses (volumes) are found to lie within or, on the contrary, to lie outside the WFW. This provides a useful alternative to a basic discretization, the latter consisting of testing a discrete (zero-dimensional) finite set of poses. In order to improve the efficiency of the computations, a means to mitigate the undesirable effects of the so-called wrapping effect is introduced. The paper also illustrates how the proposed approach is capable of dealing with small uncertainties on the geometric design parameters of a parallel cable-driven robot.

This paper presents the preliminary development of a full scale, portable, modular, fully autonomous parallel wire crane that is intended to be used for rescue operations. This design is innovative in terms of flexibility for managing the location of the anchor points of the cables on the ground and on the platform, the possibility of partial platform location control through the management of the kinematics with less than 6 cables and the availability of on-board sensors allowing to possibly locate victims through thermal imaging and to transmit physiological data on the victims while they are still moving toward a safe area.

An automated design generation algorithm for a serial kinematic chain is presented for the reconfigurable robot used in a novel endoluminal surgical procedure (European Union project ARES). The algorithm produces the possible topologies, given the design constraints, desired performance, and available modules, such that all constraints are satisfied for every point in the desired workspace. This is achieved through the use of interval analysis methods and branch-and-bound loop that searches through the end-effector pose and the design parameter spaces. The resulting algorithm is demonstrated through an example of a serial chain manipulator made of the reconfigurable modules of the surgical robot for the application. The results are presented and discussed.

This paper presents the design strategy of serial manipulators with constraint satisfaction. The algorithm provides certified solutions to the range of values of the manipulator design parameters that satisfy the given constraints for all points inside a desired workspace. Alternatively, it can also be used to obtain the achievable workspace of a particular manipulator topology within which a set of given constraints are satisfied. This strategy can therefore be applied to the general case of a serial manipulator design problem, robots of adjustable parameters, or even reconfigurable robot strategy to obtain a suitable topology. The interval-based algorithm was implemented on an example serial anthropomorphic manipulator with joint displacement constraints and obtains the possible variations to the manipulator topology that allow the required workspace to be achievable under the given joint displacement constraints. Results are presented and discussed.

Wire-driven parallel robots are special types of Gough-Stewart platform in which the rigid extensible legs are substituted by extensible wires. Usually wire length change is obtained by coiling the wire on a drum actuated by a rotary motor. We present here a robot using linear actuator and a pulley system allowing a higher modularity of the actuation system. The kinematics of this redundant system (the system has 7 wires), taking into account the elasticity of the wires, is presented. Inverse kinematics may be solved either by first choosing the wire tensions, the control vector being then a linear function of the tensions or by solving directly a system of non linear equations whose unknowns are the components of the control vector. Forward kinematics is a much more complex issue, involving the solving of a large system. We present a solving approach but this problem remains an open issue.

This paper addresses the problem of certifying the performance of a precision flexure-base mechanism design with respect to the given constraints. Due to the stringent requirements associated with the applications of flexure-based precision mechanisms, it is necessary to be able to evaluate and certify the performance at the design stage, taking into account the possible sources of errors: such as fabrication tolerance and modeling inaccuracies in flexure joints. An interval-based method is proposed to certify whether various constraints are satisfied for all points within a required workspace. This paper presents the interval-based methodology and its implementation on a planar 3RRR parallel flexure-based manipulator.

This paper reports the first results of an ongoing work which aims at providing numerical tools useful to the design of a family of high speed parallel robots. The objective is to find sets of feasible values for the design parameters unlike more usual design procedures relying on optimization techniques. These tools are mainly based on interval analysis and take into account the dynamics of the parallel robots. Moreover, they can deal with bounded uncertainties that affect some physical parameters involved in the dynamics. Following the statement of the design problems considered, a general method is presented. Then, this method is illustrated with the study of a 2-DOF parallel robot.

The wrench-feasible workspace (WFW) of a parallel cable-driven mechanism is the set of poses of its mobile platform for which the cables can balance any wrench in a specified set of wrenches, such that the tension in each cable remains within a prescribed range. The WFW is fundamental since it takes into account both the requirement of non-negative cable tension and the requirement of a maximum admissible cable tension. This paper addresses the problem of the determination of the WFW of n-degree-of-freedom parallel mechanisms driven by more than n cables. Interval analysis based methods that allow to determine if a given n-dimensional box is fully included in the WFW are presented. Moreover, these methods are also able to approximate the WFW up to a chosen accuracy. The resulting approximation consists of a set of n-dimensional boxes such that each box of the set is fully included in the WFW.

Global motion planners have been proposed for closed-loop robot based on the same paradigm than has been proposed for serial chains: a sparse representation of the configuration space of the robot is constructed as a set of nodes and a motion planning query consists simply in connecting the start and goal points through an appropriate set of nodes (usually minimizing the length of the trajectory). But such motion planner should be complemented by a local motion planner that addresses the following issues: 1) ensure that two successive nodes belong to the same robot kinematic branch (otherwise connecting these nodes will require to disassemble the robot) 2) verify that all poses between nodes satisfy the robot constraints (if possible taking into account the uncertainties in the robot modeling) 3) eventually try to shorten the trajectory length We present such a local motion planner that addresses all three issues and illustrates its use on a Gough parallel robot.

Singularity is a major problem for parallel robots as in these configurations the robot cannot be controlled, and there may be infinite forces/torques in its joints, possibly leading to its breakdown. Hence, such a configuration must usually be avoided, and certifying the absence of singularity within a prescribed workspace or on a given trajectory is essential for a practical use of this type of robots. Singularity conditions are usually quite complex, and therefore a purely analytical analysis is difficult. We present here an algorithm that combines formal and numerical calculations for detecting singularity or closeness to a singularity within an arbitrary workspace or trajectory. This algorithm has the very important advantage of being able to deal with any robot mechanical structure and to manage uncertainties in the robot control and in the robot modeling.

We are considering a 6 d.o.f. Gough platform that has to move within a given workspace or on a trajectory. The legs of the robot are assumed to be constituted of a set of finite cylindrical elements and we address the problem of determining if any pair of such element would intersect during the robot motion. Collision conditions may be written mathematically according to various equivalent formulations. We show however that these formulations are not numerically equivalent and exhibit an efficient interference checking algorithm based on interval analysis that allows to check 6D workspace or arbitrary time-function trajectories for interference

We are considering a n d.o.f. parallel robot that has to move within a given workspace and whose geometry is defined by a set of parameters. The motion of active joints of the manipulator are measured with sensors with a known accuracy ±Δρ. These errors together with bounded manufacturing errors on the parameters describing the geometry of the robot induces a positioning errors ΔX of the platform. We present an algorithm that allows one to determine geometries of the robot ensuring that these positioning errors will lie within pre-specified limits for any pose of the robot in its workspace even if the physical realization of the robot differs from the theoretical model while staying within the given manufacturing errors bounds. A by-product variant of this algorithm allows one to compute the maximal positioning errors of a given robot up to a predefined accuracy.

In this paper the problem of interference avoidance for robots subject to dynamic constraints is investigated. First computed-torque method is used to obtain a linearized closed-loop system. For this linearized system the desired state that the robot is going to take at the next sampling period is checked by phase plane analysis to ensure the robot can be stopped without interferences, dynamic constraints are taken into account by calculating the bounds of the drive torques with interval evaluation. When the desired next state is not valid for interference avoidance, a new state is scheduled by optimizing the next velocity, interval analysis is used again which allows to partition the complex constrained optimization problem into a simple two-stage problem. The resulting optimal state not only secures the robot against interference but also leads the robot to trace the desired path closely. Simulation results of a 2-DOF robot arm show the effectiveness of the proposed approach.

The workspace of a parallel robot has a complex shape and is difficult to model. Hence verifying if an arbitrary trajectory lies entirely within this workspace is a complex issue. We present an algorithm that allow such verification for any trajectory such that the pose parameters are arbitrary analytical time function. The proposed algorithm allows to check very quickly the validity of almost any trajectory (or of a surface/volume) in a guaranteed manner. Furthermore this algorithm allows one to deal with uncertainties in the followed trajectory and in the geometrical description of the robot.

Modular parallel robots are mechanisms which can adapt their geometry according to the task to be performed, usually by changing the location of the attachment points of the legs of the base. The main ideas underlying this concept are that by changing the geometry of the robot one can extend the reachable workspace and furthermore, as the performances of parallel robots are very sensitive to the geometry, it will be possible to improve the performances of the robot. We propose an algorithm which first adapt the geometry so that a set of given trajectories is included in the workspace of the robot and then optimize an arbitrary secondary criterion. We show that indeed modular parallel robot allow for drastic increase in the performances of the robot.

MIPS is a micro robot with a parallel mechanical architecture having three degrees of freedom (one translation and two orientations) that allow fine positioning of a surgical tool. The purpose of MIPS is to act as an active wrist at the tip of an endoscope and to provide to the surgeon an accurate tool that may furthermore offers a partial force-feedback. The current prototype has a diameter of 7 mm for a length of 2.5 cm and includes all the necessary hardware. We will explain why a parallel architecture has be chosen, the method of optimal design that has been used for determining the dimensions of the robot and present the current prototype.

MIPS is a micro robot with a parallel mechanical architecture having three degrees of freedom (one translation and two orientations) that allow fine positioning of a surgical tool. The purpose of MIPS is to act as an active wrist at the tip of an endoscope and to provide to the surgeon an accurate tool that may furthermore offer a partial force-feedback. The current prototype has a diameter of 7 mm for a length of 2.5 cm and includes all the necessary hardware. We will explain why a parallel architecture has be chosen, the method of optimal design that has been used for determining the dimensions of the robot and present the current prototype.

We propose an algorithm that enable one to determine almost all the geometries of a simplified Gough platform whose workspace must include an arbitrary set of poses. Five design parameters have been identified and we assume that the stroke of the linear actuator is known. This algorithm is based on an interval analysis approach and its result is a set of ranges for the design parameters such that the workspace of any robot whose geometry is defined by values within the ranges will include the specified poses.

A trend of thought in the robotics community is that most problems in kinematics have been solved and that this domain is slowly dying. The purpose of the paper is to show that there are still many unsolved problems in this field and that research on this topic may have a large influence in many different domains.

This paper presents an efficient algorithm for computing, with a guaranteed error, the maximal and minimal articular velocities of a parallel manipulator so that whatever is the location of the end-effector in a given volume it may perform a motion at a given Cartesian/angular velocity, under the assumption that its orientation is kept constant over the volume. This algorithm is much more faster and safe than the classical discretisation method.

We consider a classical Gough platform with extensible legs whose platform is submitted to a given load. This load induces forces in the linear actuators of the legs, these forces being dependent upon the posture of the platform, and we determine the extremal values of the articular forces when the platform is translating in a given 3D workspace (the orientation of the platform is assumed to be constant). We describe an efficient algorithm which enable one to compute the extremal forces more efficiently than a discretisation method.

This paper presents an algorithm for finding all the possible parallel robot geometries such that the end effector may perform a given translation velocity for any location of the end-effector in a given workspace, the constraint being that the actuator velocities should be always lower than a given bound. All these possible geometries are defined by a region in a particular design parameters space. This algorithm should be useful for the optimal design of parallel robots.

This paper presents a design methodology for parallel robots having to satisfy a set of performance constraints. After a reduction of the number of the design parameters some performance requirements are used to compute a closed region in the parameter space (in which a point define a unique robot geometry) which contains all the robot geometries satisfying the requirements. The requirements which have not been used in the first step are described then, in a high level language procedure which takes the robot geometry as input, determine if the robot fulfil the users requirements. The closed region determined at the first step is then discretized and the robot geometry which corresponds to each node of the discretisation is submitted to the procedure. The node leading to the robot(s) fulfilling at best the constraints is the design solution.

In this paper a new architecture of a planar three-degree-of-freedom (3-dof) parallel manipulator is presented. In the proposed mechanism, the prismatic actuators are fixed to the base which leads to a reduction of the inertia of the moving links and hence makes it attractive, particularly when high speeds are required and electric actuation is considered. After introducing the mechanism, a kinematic analysis is reported. Then, velocity and acceleration equations are derived. Based on the geometry of the manipulator a workspace analysis is performed and a description of the boundaries of the workspace is provided. This manipulator can be used in robotic applications involving the positioning and orientation of a rigid body on the plane with high stiffness or accuracy. Additionally, the mechanism can find applications in motion simulators or other high-precision or high-speed devices.

Presents a method for designing optimal parallel manipulators of the Gough platform type, according to design constraints like a specified workspace, best accuracy over the workspace, minimum articular forces for a given load, etc. A reduced set of design parameters is defined and the workspace constraints are used to compute the zone of the parameters space which define all the robots whose workspace include the desired workspace. Then a numerical search is performed in this zone to determine the robot which optimize some other criterion. The author shows how the method has been used to design a robot whose accuracy was specified to be better than 1 /spl mu/m for a nominal load of 500 kg.

We address the problem of finding all the solutions of the direct kinematics for every possible architectures of planar fully parallel manipulators. We show that for this problem all the possible kinematic chains can be reduced to a set of three basic chains and we explain how to calculate the solutions of the forward kinematics for all the combinations of these basic chains and consequently for all the possible architectures of planar parallel robots.

We consider a Stewart platform and show that its forward kinematics has at most 12 solutions. A first geometrical demonstration is provided which uses the concept of circularity and in a second proof we show that this problem is equivalent to find a system of two planar parallel manipulators with each 6 solutions to the forward kinematic problem. A geometrical construction is provided to construct such a system and a Stewart platform with 12 configurations is exhibited.>

We present a fast algorithm for solving the problem of determining if the straight line between two different postures of a parallel manipulator lie fully inside its workspace. This algorithm is based on the analysis of the algebraic inequalities describing the constraints on the workspace (link lengths range, mechanical limits on the joints, interference between the links) and enables to compute which part of the trajectory is outside the workspace. This method is exact if the orientation of the end-effector is kept constant along the trajectory and approximate in the opposite case.>

The determination of the direct kinematics of fully parallel manipulators is in general a difficult problem but has to be solved for any practical use. Various methods are presented to solve this problem: two kinds of iterative schemes, a reduced iterative scheme, and a polynomial method. The computation time of these methods are compared and their various advantages are shown.>

The author considers a specific parallel manipulator and determines the features of the infinitesimal motions associated with each of the singular configurations. It is shown that every singular configuration for a MSSM is obtained when the 6 lines associated with the links of the manipulator belong to a linear complex of lines. Consequently, it is known that the corresponding infinitesimal motion is a screw motion. If the complex is singular (as in Hunt's configuration) the pitch of this motion is equal to zero and therefore the resulting motion is a pure rotation around the ISA (which is the line intersecting all 6 lines of the manipulator). If the complex is general, one has determined the ISA and the pitch of the screw motion when the base and mobile plates are parallel.>

A light parallel manipulator currently under development at INRIA is presented. The problems of its singular configurations and its direct kinematics have been addressed. A geometrical approach makes it possible to find the constraint equations on the generalized coordinate vector such that the resulting configuration of the manipulator is singular. This approach will make it possible to determine if some of the singular configurations lie in the workspace of the manipulator. It is shown that the direct kinematic problem has up to 16 solutions, and a set of particular coordinates is exhibited for which the mobile plate may effectively be in 16 different positions.>

The main features of a parallel manipulator are summarized, and it is shown that their passive compliance can be completely controlled. This feature is particularly important for improving the efficiency of force-feedback control methods and the stability. A prototype parallel manipulator is designed which includes force sensing. A novel force-feedback method is implemented and assembly experiments are performed with parts of various shape and rigidity and with very tight clearance (less than 10 mu ). One purpose of these experiments was to determine the importance of the passive compliance of the manipulator. It is shown clearly that the force-feedback method greatly improves the insertion process.>

C-surfaces are defined in the parameter's space by the border between the subspace where the robot's positions are constrained by the surrounding and the subspace where there is no contact. Thus force control must be performed along the C-surface normal and position control along the tangent hyperplane of the C-surface. We have shown that the C-surface normal can be calculated by the use of force measurements. This yield to the design of an hybrid force-position controller where the direction to be force controlled is automatically determined. Experimental results are presented and compared to simulation for the surface following problem. Assembly tasks and the turning of a crank have been executed in simulation by using this hybrid controller. Experiments with a parallel manipulator are currently under development.