Josef Schadlbauer

Kinematic Analysis of the 3-RPS Cube Parallel Manipulator

The 3-RPS Cube parallel manipulator, a three-degree-of-freedom parallel manipulator initially proposed by Huang et al. in 1995, is analysed in this paper with an algebraic approach, namely Study kinematic mapping of the Euclidean group SE(3) and is described by a set of eight constraint equations. A primary decomposition is computed over the set of eight constraint equations and reveals that the manipulator has only one operation mode. Inside this operation mode, it turns out that the direct kinematics of the manipulator with arbitrary values of design parameters and joint variables, has sixteen solutions in the complex space. A geometric interpretation of the real solutions is given. The singularity conditions are obtained by deriving the determinant of the Jacobian matrix of the eight constraint equations. All the singular poses are mapped onto the joint space and are geometrically interpreted. By parametrizing the set of constraint equations under the singularity conditions, it is shown that the manipulator is in actuation singularity. The uncontrolled motion gained by the moving platform is also provided. * corresponding author, Paper JMR-14-1262, corresponding authors last name: CARO 1 The motion of the moving platform is essentially determined by the fact that three vertices in the moving platform move in three mutually orthogonal planes. The workspace of each point of the moving platform (with exception of the three vertices) is bounded by a Steiner surface. This type of motion has been studied by Darboux in 1897. Moreover, the 3-dof motion of the 3-RPS Cube parallel manipulator contains a special one-degree-of-freedom motion, called the Vertical Darboux Motion. In this motion, the moving platform can rotate and translate about and along the same axis simultaneously. The surface generated by a line in the moving platform turns out to be a right-conoid surface.

Kinematic Analysis of an Innovative Medical Parallel Robot Using Study Parameters

The paper investigates the kinematic analysis of an innovative 5-DOF parallel medical robot used for brachytherapy. Robotic assisted brachytherapy involves the targeted treatment of cancerous cells delivering high dosages of radiation inside the tumor, using as guiding tool a highly accurate robotic arm. The kinematic modeling of this mechanism is addressed using algebraic constraint varieties and the Study parametrization of the Euclidean displacement group. Algebraic methods in connection with classical multi-dimensional geometry have proven to be very efficient in the computation of direct and inverse kinematics of mechanisms as well as the explanation of strange, pathological behavior. The obtained results are simulated and compared with the results obtained by the evaluation of the determinants of the A and B Jacobi matrices. This complete kinematic analysis of the robot will largely increase its safety during the medical procedure.

Operation Modes in Lower-Mobility Parallel Manipulators

This paper discusses the notion of operation mode in parallel manipulators with less than six dof. This notion has been reported recently in several papers but the physical meaning of an operation mode is not always clear. Indeed, even if in some cases an operation mode can be associated with an understandable motion type e.g., three pure translations or a spherical motion, in some other cases, such an association is not straightforward. Therefore, the axodes are used in this paper to characterize any operation mode of lower-mobility parallel manipulators. A 3-RPS manipulator is used as an illustrative example. This manipulator is special because one can parameterize its operation modes.

Motion Capability of the 3-RPS Cube Parallel Manipulator

This chapter deals with the analysis of motion capability of the 3-RPS Cube parallel manipulator. The constraint equations of the manipulator are first expressed and it is shown that its moving-platform is capable of any orientation determined by a three parameter set \(u,v,w\). The translation part of the motion is coupled to these three parameters. It is shown that this type of three dof motion has been studied by Darboux in 1897. Moreover, the moving-platform can perform the Vertical Darboux Motion, namely, it can rotate and translate about and along the same axis simultaneously. The surface generated by the moving-platform path turns out to be a right-conoid. The axodes generated by the motion are two coinciding lines passing through the origin of the fixed frame.

The 3-RPS Manipulator Can Have Non-Singular Assembly-Mode Changes

Recently a complete kinematic description of the \(3\)-RPS parallel manipulator was obtained using algebraic constraint equations. It turned out that the workspace decomposes into two components describing two kinematically different operation modes and that self-motions of this manipulator in both operation are possible. In this paper for the first time it is shown that this manipulator has the property of non singular assembly mode change.

A Complete Analysis of Singularities of a Parallel Medical Robot

This paper analyzes the singular poses of a 5-DOF parallel robot used for brachytherapy. In compliance with the latest safety protocols and requirements [3] the paper presents a new mathematical model using algebraic constraints and the Study parameterization of the Euclidian displacement group. Using algebraic methods combined with multidimension geometry proved to be efficient in the calculation of the kinematics of mechanisms and in the explanations of their behavior. The results obtained using this algebraic method were analyzed with respect to the data obtained from the experimental model of the robot by comparing theoretical computation results with the actual behavior of the robot. The analysis of the kinematics using these methods allows a complete description of working modes, singularities and robot behavior enabling a safe control throughout the medical task.

A New Approach to the Direct Geometrico-Static Problem of Cable Suspended Robots Using Kinematic Mapping

The direct kinematic problem of \(n-n\ (n=2,3,4,5)\) underconstrained cable manipulators has been solved previously by exploiting the line geometric equilibrium condition and using optimization techniques, heavy algebraic or numeric algebraic computation. In this paper another solution method is proposed. It uses kinematic mapping, distance constraint equations and a local plane constraint. This method can be used for all cases of underconstrained cable manipulators and it is also applicable to the case of \(n-i\) equilibria of \(n-\)cable manipulators. Univariate polynomials are computed in examples for the \(3-3\) and \(5-5\) cases as well as for \(n-1\) equilibria of the \(5-5\) case.

The Instantaneous Screw Axis of Motions in the Kinematic Image Space

In the velocity analysis of mechanisms the instantaneous screw axes and the corresponding axodes play an important role. The instantaneous screw axis is computed via the velocity operator, this is the skew-symmetric matrix \(\mathbf {\dot{A} A^T }\), where \(\mathbf {A}\) is the transformation matrix. From this operator the Plucker coordinates of the instantaneous screw axis are known. When the Study parameters of a one parametric motion are given a direct computation of the instantaneous screw axis would be more convenient. Without computing \(\mathbf {A}\) and its derivative first, this paper shows a way of computing the instantaneous screw axis directly from the Study parameterization of the one parametric motion.