Non-singular assembly mode changing trajectories in the workspace for the 3-RPS parallel robot

Having non-singular assembly modes changing trajectories for the 3-RPS parallel robot is a well-known feature. The only known solution for defining such trajectory is to encircle a cusp point in the joint space. In this paper, the aspects and the characteristic surfaces are computed for each operation mode to define the uniqueness of the domains. Thus, we can easily see in the workspace that at least three assembly modes can be reached for each operation mode. To validate this property, the mathematical analysis of the determinant of the Jacobian is done. The image of these trajectories in the joint space is depicted with the curves associated with the cusp points

An algebraic method to check the singularity-free paths for parallel robots

Trajectory planning is a critical step while programming the parallel manipulators in a robotic cell. The main problem arises when there exists a singular configuration between the two poses of the end-effectors while discretizing the path with a classical approach. This paper presents an algebraic method to check the feasibility of any given trajectories in the workspace. The solutions of the polynomial equations associated with the tra-jectories are projected in the joint space using Gr{\"o}bner based elimination methods and the remaining equations are expressed in a parametric form where the articular variables are functions of time t unlike any numerical or discretization method. These formal computations allow to write the Jacobian of the manip-ulator as a function of time and to check if its determinant can vanish between two poses. Another benefit of this approach is to use a largest workspace with a more complex shape than a cube, cylinder or sphere. For the Orthoglide, a three degrees of freedom parallel robot, three different trajectories are used to illustrate this method.Comment: Appears in International Design Engineering Technical Conferences & Computers and Information in Engineering Conference , Aug 2015, Boston, United States. 201

Workspace and joint space analysis of the 3-RPS parallel robot

International audienceThe Accurate calculation of the workspace and joint space for 3 RPS parallel robotic manipulator is a highly addressed research work across the world. Researchers have proposed a variety of methods to calculate these parameters. In the present context a cylindrical algebraic decomposition based method is proposed to model the workspace and joint space. It is a well know feature that this robot admits two operation modes. We are able to find out the set in the joint space with a constant number of solutions for the direct kinematic problem and the locus of the cusp points for the both operation mode. The characteristic surfaces are also computed to define the uniqueness domains in the workspace. A simple 3-RPS parallel with similar base and mobile platform is used to illustrate this method

Workspace and joint space analysis of the 3-RPS parallel robot

International audienceThe Accurate calculation of the workspace and joint space for 3 RPS parallel robotic manipulator is a highly addressed research work across the world. Researchers have proposed a variety of methods to calculate these parameters. In the present context a cylindrical algebraic decomposition based method is proposed to model the workspace and joint space. It is a well know feature that this robot admits two operation modes. We are able to find out the set in the joint space with a constant number of solutions for the direct kinematic problem and the locus of the cusp points for the both operation mode. The characteristic surfaces are also computed to define the uniqueness domains in the workspace. A simple 3-RPS parallel with similar base and mobile platform is used to illustrate this method

Influence of the trajectory planning on the accuracy of the orthoglide 5-axis

International audienceUsually, the accuracy of parallel manipulators depends on the architecture of the robot, the design parameters, the trajec-tory planning and the location of the path in the workspace. This paper reports the influence of static and dynamic parameters in computing the error in the pose associated with the trajectory planning made and analyzed with the Orthoglide 5-axis. An error model is proposed based on the joint parameters (velocity and acceleration) and experimental data coming from the Or-thoglide 5-axis. Newton and Gröbner based elimination methods are used to project the joint error in the workspace to check the accuracy/error in the Cartesian space. For the analysis, five similar trajectories with different locations inside the workspace are defined using fifth order polynomial equation for the trajec-tory planning. It is shown that the accuracy of the robot depends on the location of the path as well as the starting and the ending posture of the manipulator due to the acceleration parameters

Workspace, Joint space and Singularities of a family of Delta-Like Robot

International audienceThis paper presents the workspace, the joint space and the singularities of a family of delta-like parallel robots by using algebraic tools. The different functions of SIROPA library are introduced, which is used to induce an estimation about the complexity in representing the singularities in the workspace and the joint space. A Groebner based elimination is used to compute the singularities of the manipulator and a Cylindrical Algebraic Decomposition algorithm is used to study the workspace and the joint space. From these algebraic objects, we propose some certified three-dimensional plotting describing the shape of workspace and of the joint space which will help the engineers or researchers to decide the most suited configuration of the manipulator they should use for a given task. Also, the different parameters associated with the complexity of the serial and parallel singularities are tabulated, which further enhance the selection of the different configuration of the manipulator by comparing the complexity of the singularity equations

The fast declining Type Ia supernova 2003gs, and evidence for a significant dispersion in near-infrared absolute magnitudes of fast decliners at maximum light

We obtained optical photometry of SN 2003gs on 49 nights, from 2 to 494 days after T(B_max). We also obtained near-IR photometry on 21 nights. SN 2003gs was the first fast declining Type Ia SN that has been well observed since SN 1999by. While it was subluminous in optical bands compared to more slowly declining Type Ia SNe, it was not subluminous at maximum light in the near-IR bands. There appears to be a bimodal distribution in the near-IR absolute magnitudes of Type Ia SNe at maximum light. Those that peak in the near-IR after T(B_max) are subluminous in the all bands. Those that peak in the near-IR prior to T(B_max), such as SN 2003gs, have effectively the same near-IR absolute magnitudes at maximum light regardless of the decline rate Delta m_15(B). Near-IR spectral evidence suggests that opacities in the outer layers of SN 2003gs are reduced much earlier than for normal Type Ia SNe. That may allow gamma rays that power the luminosity to escape more rapidly and accelerate the decline rate. This conclusion is consistent with the photometric behavior of SN 2003gs in the IR, which indicates a faster than normal decline from approximately normal peak brightness.Comment: 41 pages, 13 figures, to be published in the December, 2009, issue of the Astronomical Journa

A search for transients in the Reionization Lensing Cluster Survey (RELICS): Three new supernovae

The Reionization Cluster Survey (RELICS) imaged 41 galaxy clusters with the Hubble Space Telescope (HST), in order to detect lensed and high-redshift galaxies. Each cluster was imaged to about 26.5 AB mag in three optical and four near-infrared bands, taken in two distinct visits separated by varying time intervals. We make use of the multiple near-infrared epochs to search for transient sources in the cluster fields, with the primary motivation of building statistics for bright caustic crossing events in gravitational arcs. Over the whole sample, we do not find any significant ($\gtrsim5 \sigma$) caustic crossing events, in line with expectations from semi-analytic calculations but in contrast to what may be naively expected from previous detections of some bright events, or from deeper transient surveys that do find high rates of such events. Nevertheless, we find six prominent supernova (SN) candidates over the 41 fields: three of them were previously reported and three are new ones reported here for the first time. Out of the six candidates, four are likely core-collapse (CC) SNe -- three in cluster galaxies, and among which only one was known before, and one slightly behind the cluster at $z\sim0.6-0.7$. The other two are likely Ia -- both of them previously known, one probably in a cluster galaxy, and one behind it at $z\simeq2$. Our study supplies empirical bounds for the rate of caustic crossing events in galaxy cluster fields to typical HST magnitudes, and lays the groundwork for a future SN rate study.Comment: Accepted for publication in MNRAS. 10 pages, 3 figure