Latifah Nurahmi

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.

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.

Comparison of 3-RPS and 3-SPR Parallel Manipulators Based on Their Maximum Inscribed Singularity-Free Circle

This paper deals with the comparison of 3-RPS and 3-SPR parallel manipulators based on their operation modes and singularity-free workspace. The operation modes of the 3-SPR manipulator are identified by using algebraic geometry. Those operation modes amount to the operation modes of the 3-RPS parallel manipulator, which has already been studied in the literature [1]. Then, the parallel singularities of the 3-SPR and 3-RPS parallel manipulators are analyzed in order to trace their singularity loci throughout their orientation workspace. An index, named Maximum Inscribed Circle Radius (MICR), is defined to compare the two manipulators under study. It is based on their maximum singularity-free workspace and the ratio between their circum-radius of the moving-platform to that of the base.

Operation Modes and Singularities of 3-PRS Parallel Manipulators With Different Arrangements of P-Joints

The subject of this paper is about the study of the operation modes and the singularity conditions of the 3-PRS parallel manipulator with different arrangements of prismatic joints. The three prismatic joints of the PRS legs are attached to the base with an angle α between the horizontal plane of the base and their directions.By using an algebraic approach, namely the Study kinematic mapping of the Euclidean group SE(3), the mechanisms are described by a set of eight constraint equations. A primary decomposition is computed over a set of eight constraint equations and reveals that the 3-PRS manipulators with different arrangements of prismatic joints have identical operation modes, namely x0 = 0 and x3 = 0. Both operation modes are analysed.The singularity conditions are obtained by deriving the determinant of the Jacobian matrix of the eight constraint equations. All the singular configurations are mapped onto the joint space and are geometrically interpreted. The singularity loci of the 3-PRS parallel manipulators are also traced in its orientation workspace for different values of angle α.Copyright

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.

Dimensionally Homogeneous Jacobian and Condition Number

This paper deals with the formulation of the dimensionally homogeneous extended Jacobian matrix, which is an important issue for the performance analysis of f degrees-of-freedom (f ≤6) parallel manipulators having coupled rotational and translational motions. By using the f independent coordinates to define the permitted motions and (6-f) independent coordinates to define the restricted motions of the moving platform, the 6×6 dimensionally homogeneous extended Jacobian matrix is derived for non-redundant parallel manipulators. The conditioning number of the parallel manipulators is computed to evaluate the homogeneous extended Jacobian matrix, the homogeneous actuation wrench matrix, and the homogeneous constraint wrench matrix to evaluate the performance of the parallel manipulators. By using these indices, the closeness of a pose to different singularities can be detected. An illustrative example with the 3-RPS parallel manipulator is provided to highlight the effectiveness of the approach and the proposed indices.

Conceptual Design of Schoenflies Motion Generators Based on the Wrench Graph

The subject of this paper is about the conceptual design of parallel Schoenflies motion generators based on the wrench graph.By using screw theory and Grassmann geometry, some conditions on both the constraint and the actuation wrench systems are generated for the assembly of limbs of parallel Schoenflies motion generators, i.e., 3T1R parallel manipulators. Those conditions are somehow related to the kinematic singularities of the manipulators. Indeed, the parallel manipulator should not be in a constraint singularity in the starting configuration for a valid architecture, otherwise it cannot perform the required motion pattern. After satisfying the latter condition, the parallel manipulator should not be in an actuation singularity in a general configuration, otherwise the obtained parallel manipulator is permanently singular.Based on the assembly conditions, six types of wrench graphs are identified and correspond to six typical classes of 3T1R parallel manipulators. The geometric properties of these six classes are highlighted. A simplified expression of the superbracket decomposition is obtained for each class, which allows the determination and the comparison of the singularities of 3T1R parallel manipulators at their conceptual design stage. The methodology also provides new architectures of parallel Schoenflies motion generators based on the classification of wrench graphs and on their singularity conditions.Copyright

Design optimization of spatial four cables suspended cable driven parallel robot for rapid life-scan

This paper presents the dimension optimization of spatial suspended Cable Driven Parallel Robot (CDPR), with only four cables. The dimension of mobile platform as well as the positions of anchor points on to the mobile platform will be optimized, hence the mobile platform will be able to carry a thermal sensor for rapid-life-scan in the disaster area. The CDPR analyzed in this paper is suspended, thus the dimensioning of mobile platform is related to the performance of CDPR, namely its static and kinematic equilibrium. Six different case studies are investigated to determine the dimension of mobile platform and the positions of exit points on the mobile platform on to the mobile platform that minimize the maximum cable tensions and the maximum cable velocities.

Dimension synthesis of 3-RPS parallel manipulator with intersecting R-axes for ankle rehabilitation device

This paper deals with the development and dimension synthesis of the 3-RPS parallel manipulator for ankle rehabilitation device. The architecture of the 3-RPS parallel manipulator was achieved through novel methodology introduced in [1]. Three revolute axes intersect at one point. This point being the center of rotation of the ankle rehabilitation device and it will be placed as close as possible to the ankle joint. By using the Euler parametrization, the dimension of the base and the platform will be synthesized by considering its orientation capability. The singularities will be the constraint of the synthesis process. Using the synthesis method introduced in this paper, the novel 3-RPS parallel manipulator is provided.

Operation modes and self-motion of 2-RUU parallel manipulator

This paper deals with the characterisation of the operation modes of the 2-RUU parallel manipulator with an algebraic approach, namely the studys kinematic mapping of the Euclidean group SE(3). The manipulator is described by a set of eight constraint equations and the primary decomposition reveals that the mechanism has three 4-dof operation modes. The singularity conditions are obtained by deriving the determinant of the Jacobian matrix of the constraint equations with respect to the study parameters. It is shown that there exist singular configurations in which the 2-RUU parallel manipulator may switch from one operation mode to another operation mode, which is known as constraint singularity. All the singular configurations are mapped onto the joint space and are physically interpreted. Eventually, the 2-RUU parallel manipulator may switch from the 1st Schonflies mode to the 2nd Schonflies mode, or vice versa, through the additional 4-dof mode that contains self-motion.