Parallel robots play an important role in the industry nowadays, as witnessed by an increasing growth in a variety of their applications. However, the analyses of their kinematics, workspace, and singularities are of considerable complexity versus serial robots, as some of the problems in this field have been remained unsolved. Confrontation with singularities of parallel robots can be expressed in terms of three different approaches, namely: 1) synthesis considerations for designing mechanisms with fewer singularities 2) obtaining largest singularity-free zones within the workspace of the mechanisms to ensure the safety of these regions from singularity 3) to consider the singularity in the path generation procedure to obtain singularity-free paths. In this thesis, it is aimed at exerting analytical methods based on convex optimization to resolve problems caused by the singularities in the workspace of the mechanisms, including failure to implement control algorithms, collapse of mechanism configuration, and damage to the mechanical components of the robot.

 
This project introduces a new general systematic approach, which is based on the so-called triangle-to-triangle intersection test, in order to obtain the collision-free workspace of robotic mechanical systems. In the proposed geometric constructive approach, a collision test will be performed on the STL file for all possible configurations of the robot which leads to obtaining the collision-free workspace. In this approach, by introducing a bounding sphere, from the obtained results it reveals that the computational time on average is 0.049 μs per test which is reduced by 23% comparing to one of the recent algorithm proposed in the literature. Furthermore, the collision-free workspace determination approach provides a statistical data about the percentage of collision for each constituting part of the mechanism. By resorting to the latter statistical data, an index for collision-free workspace is introduced which provides some insights into designing a well-conditioned workspace in terms of mechanical interference.

Collision-free workspace of 3-RRR parallel mechanism.

The 3-RRR Planar Parallel Mechanism is designed, constructed and controlled in Human and Robot Interaction Laboratory. The focus is on experimental control methods using inverse kinematic problem in order to gain more accuracy and smooth movement during the control process. Since there is no direct feedback sensor on the end-effector, all the foregoing control approaches could be regarded as open-loop control. In order to control the mechanism, two main control methods are used namely, position control and speed control. A Joy-stick is added to the system, in order to provide the ability for the user to control the mechanism directly. In addition, a Graphical User Interface is designed to help the user by three main control states. The first state is considered as off-line control, in which, the mechanism will follow a specific path defined in the program. In the second state, off-line control via Joy-stick, the mechanism will follow a path specified by the user via Joy-stick. As the third state, which is considered as the on-line control via Joy-stick, the mechanism will interactively follow a path specified by the user via the Joy-stick. All the programs are written in Qt creator in order to speed up data transmission from computer to the mechanism’s actuators and vice versa.

 
In this research, as the main contribution, a comprehensive study is carried out on the mathematical modeling and analysis of the inverse kinematics and dynamics of an over-constraint three translational degree-of-freedom parallel manipulator. Since dynamic formulation of over-constraint parallel manipulators do not admit solution, due to the inconsistency between the number of equations and unknowns, thus the problem has initiated many challenges. In order to obtain a dynamical model, and circumvent the problem of inconsistency between the number of equations and unknowns, a modification is applied in the kinematic arrangement of the under study manipulator by preserving the performed motion pattern. Then, the dynamical equations of the manipulator are obtained based on the Newton–Euler approach and a simple and compact formulation is provided and all the joint forces and torques are presented. In order to evaluate the accuracy of the obtained formulated model, a motion for the end-effector as case study is performed, and it has been shown that the results of the analytical model are in good agreement with those obtained from SimMechanics model.

Vector notation for the kinematic modeling of the Tripteron.