Singularity Locus for the Endpoint Map of Serial Manipulators with Revolute Joints

We present a theoretical and algorithmic method for describing the singularity locus for the endpoint map of any serial manipulator with revolute joints. As a surface of revolution around the first joint, the singularity locus is determined by its intersection with a fixed plane through the first joint. The resulting plane curve is part of an algebraic curve called the singularity curve. Its degree can be computed from the specialized case of all pairs of consecutive joints coplanar, when the singularity curve is a union of circles, counted with multiplicity two. Knowledge of the degree and a simple iterative procedure for obtaining sample points on the singularity curve lead to the precise equation of the curve. © Springer Science+Business Media Dordrecht 2014

Realistic Rendering of Kinetostatic Indices of Mechanisms

International audienceThe work presented in this paper is related to the use of a haptic device in an environment of robotic simulation. Such device introduces a new approach to feel and to understand the boundaries of the workspace of mechanisms as well as its kinetostatic properties. Indeed, these concepts are abstract and thus often difficult to understand for the end-users. To catch his attention, we propose to amplify the problems of the mechanisms in order to help him to take the good decisions

Incorporation of the influences of kinematics parameters and joints tilting for the calibration of serial robotic manipulators

Serial robotic manipulators are calibrated to improve and restore their accuracy and repeatability. Kinematics parameters calibration of a robot reduces difference between the model of a robot in the controller and its actual mechanism to improve accuracy. Kinematics parameter’s error identification in the standard kinematics calibration has been configuration independent which does not consider the influence of kinematics parameter on robot tool pose accuracy for a given configuration. This research analyses the configuration dependent influences of kinematics parameters error on pose accuracy of a robot. Based on the effect of kinematics parameters, errors in the kinematics parameters are identified. Another issue is that current kinematics calibration models do not incorporate the joints tilting as a result of joint clearance, backlash, and flexibility, which is critical to the accuracy of serial robotic manipulators, and therefore compromises a pose accuracy. To address this issue which has not been carefully considered in the literature, this research suggested an approach to model configuration dependent joint tilting and presents a novel approach to encapsulate them in the calibration of serial robotic manipulators. The joint tilting along with the kinematics errors are identified and compensated in the kinematics model of the robot. Both conventional and proposed calibration approach are tested experimentally, and the calibration results are investigated to demonstrate the effectiveness of this research. Finally, the improvement in the trajectory tracking accuracy of the robot has been validated with the help of proposed low-cost measurement set-up.Thesis (M.Phil.) (Research by Publication) -- University of Adelaide, School of Mechanical Engineering , 201

Design and analysis of kinematically redundant planar parallel manipulator for isotropic stiffness condition

Parallel manipulators are a form of closed loop linkages and have a wide range of applications e.g. surgical robots, flight simulators, pointing devices etc. Parallel mechanisms have many advantages over serial manipulator. Higher accuracy, stiffness and increased payload capacity are the characteristics of parallel manipulator. In spite of many advantages, they have limited workspace and more singularity regions. So, redundant architectures have become popular. However, redundancy leads to infinite solutions for inverse kinematic problem. The current work addresses this issue of resolving the redundancy of kinematically redundant planar parallel manipulators using optimization based approach. First the conventional non-redundant 3-RPR planar parallel manipulator is presented. Afterwards the kinematically redundant counterpart 3-PRPR is discussed and actuation redundant 4-RPR has been touched upon briefly. Computer simulations have been performed for the kinematic issues using MATLAB programme . The workspace of redundant and non-redundant parallel manipulators have been obtained. The generalized stiffness matrix has been derived based upon the Jacobian model and the principle of duality between kinematics and statics. A stiffness index has been formulated and the isotropy of stiffness index is used as the criterion for resolving redundancy. A novel spiral optimization metaheuristics has been used to achieve the isotropic stiffness within the selected workshape and the results are compared against particle swarm optimization. The results obtained from the novel Spiral optimization are found to be more effective and closer to the objective function as compared to the particle swarm optimization. Optimum redundant parameters are obtained as a result of the analysis. A wooden skeletal prototype has also been fabricated to enhance the understanding of the mechanism workability

Reconfiguration and tool path planning of hexapod machine tools

Hexapod machine tools have the potential to achieve increased accuracy, speed, acceleration and rigidity over conventional machines, and are regarded by many researchers as the machine tools of the next generation. However, their small and complex workspace often limits the range of tasks they can perform, and their parallel structure raises many new issues preventing the direct use of conventional tool path planning methods. This dissertation presents an investigation of new reconfiguration and tool path planning methods for enhancing the ability of hexapods to adapt to workspace changes and assisting them in being integrated into the current manufacturing environments. A reconfiguration method which includes the consideration of foot-placement space (FPS) determination and placement parameter identification has been developed. Based on the desired workspace of a hexapod and the motion range of its leg modules, the FPS of a hexapod machine is defined and a construction method of the FPS is presented. An implementation algorithm for the construction method is developed. The equations for identifying the position and orientation of the base joints for the hexapod at a new location are formulated. For the position identification problem, an algorithm based on Dialytic Elimination is derived. Through examples, it is shown that the FPS determination method can provide feasible locations for the feet of the legs to realize the required workspace. It is also shown that these identification equations can be solved through a numerical approach or through Dialytic Elimination using symbolic manipulation. Three dissimilarities between hexapods and five-axis machines are identified and studied to enhance the basic understanding of tool path planning for hexapods. The first significant difference is the existence of an extra degree of freedom (γ angle). The second dissimilarity is that a hexapod has a widely varying inverse Jacobian over the workspace. This leads to the result that a hexapod usually has a nonlinear path when following a straight-line segment over two sampled poses. These factors indicate that the traditional path planning methods should not be used for hexapods without modification. A kinematics-based tool path planning method for hexapod machine tools is proposed to guide the part placement and the determination of γ angle. The algorithms to search for the feasible part locations and γ sets are presented. Three local planning methods for the γ angle are described. It is demonstrated that the method is feasible and is effective in enhancing the performance of the hexapod machine. As the nonlinear error is computationally expensive to evaluate in real time, the measurement of total leg length error is proposed. This measure is proved to be effective in controlling the nonlinear error

Motion/Force transmission analysis of axis-symmetric parallel mechanisms with closed-loop sub-chains

 This thesis presents several results regarding the kinematic performance analysis of axis-symmetric parallel mechanisms with closed-loop sub-chains. Screw theory based methods have been utilised to generate new indices, along with a formal procedure, enabling the systematic and complete singularity and motion/force transmission analysis of parallel mechanisms with these closed-loop sub-chains