Although classical and preliminary kinematic investigations of robotic mechanical systems are the principal goal Human and Robot Interaction laboratory, resorting to algebraic geometry is essential because problems eventually became elusive to classical approaches. The use of algebraic geometry leads to some groundbreaking results which could be astonishing. The alternation of perspectives is prominently present in the different projects.
Thus, as a global objective, Human and Robot Interaction Laboratory aims at reconciling two nearly disconnected communities, namely the geometricians and mechanical engineers. With that in mind,all the theoretical objectives about the kinetostatic analysis of robotic mechanical systems are treated by veering a little from our engineering grounding and using algebraic geometry concepts, such as sevendimensional kinematic space (the socalled Study's parameters), GrassmannCayley Algebra and Screw Theory. To achieve the aforementioned global objective, the obtained results are also reexplored using engineering vision to ﬁll some gaps that geometrical treatments fails to provide in a design context.
Singularity Analysis of Parallel Manipulators using GrassmannCaylay Algebra
People Involved 
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Singularity Analysis has always been an important topic to robotics researchers and is an active research field since part of controlling a robot is to avoid the singular points. Here at Taarlab we propose the new methods of dealing with this area of research by using the modern technics borrowed from Geometrical Algebra. The efficiency of these methods are to their simplicity and being coordinatefree.


Analysis of the forward kinematic of the 4DOF spatial parallel robots with identical limb structures and specified motion pattern of 3T1R
People Involved 
, Davood Naderi

A parallel robot is a closedloop kinematic chain mechanism whose moving platform is linked to the base by at least two independent kinematic chains. Due to the resulting system of nonlinear equations, the Forward Kinematic Problem (FKP) of parallel robots is complicated and cannot be easily analyzed. This thesis investigates the FKP of 4DOF parallel robots with identical kinematic chain structures performing three translations and one rotation motion pattern, referred to as Schönflies motion. These robots have a short history and very few studies have been conducted on their kinematic characteristics. Based on the complexity of the FKP of 4DOF parallel robots, the proposed algorithms are implemented on 3DOF planar parallel robots, which are simpler structures, and then they are applied on 4DOF parallel robots. First, the FKP of the parallel robots are studied in threedimensional Euclidean space. In this approach, the joint position, kinematic constraints and resultant method are used for analysis of the FKP of parallel robots. Moreover, for the sake of comparison, the system of equations corresponding to the forward kinematic problem is solved upon resorting to Bertini software and inverse kinematic problem. Then, the FKP of parallel robots are investigated in sevendimensional kinematic space. In this method, the FKP is analyzed by means of DenavitHartenberg parameters, Study’s kinematic mapping, LIA algorithm and Gröbner basis. The solutions of the FKP in sevendimensional kinematic space are mapped to the threedimensional Euclidean space and compared to the obtained results from resultant method. More, a new algorithm is presented in sevendimensional kinematic space by means of Euler’s parameters, LIA method and interval analysis, so that this algorithm analyzes the FKP of parallel robots considering to the motion range of passive joints. The results obtained from new algorithm are compared with the results of the presented method in sevendimensional kinematic space and fully confirmed the validity.

