CollisionFree Workspace Determination via TriangletoTriangle Intersection Test
People Involved 
and Nima Karbasizadeh

This project introduces a new general systematic approach, which is based on the socalled triangletotriangle intersection test, in order to obtain the collisionfree 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 collisionfree 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 collisionfree 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 collisionfree workspace is introduced which provides some insights into designing a wellconditioned workspace in terms of mechanical interference.

Collisionfree workspace of 3RRR parallel mechanism.
A 3RRR planar manipulator meshed with triangles in STL file. 
Dynamic modeling and base inertial parameters determination of 2DOF TezGoz
People Involved 
and Alaleh Arian

This project deals with the dynamic modeling and base inertial parameter determination of a general 5R 2degreeoffreedom spherical parallel manipulator. By using a new geometric approach, inverse and forward kinematic problem are transformed to the problem of determining the intersection of two cones with common vertex. Compared to other proposed methods, this approach yields more compact and closedform solutions. The instantaneous kinematic and acceleration problem is solved via employing the screw theory. The dynamic model is formulated by means of the principle of virtual work and the concept of link Jacobian matrices. In order to verify the proposed methods and equations, a case study is performed, in which an orthogonal 2DOF SPM, named TezGoz, is considered. Performed simulations and comparisons with a SimMechanics model show the correctness of the derived equations. Furthermore, a reduced dynamic model is obtained by determining the base inertial parameters. To do so, first the dynamic model is rewritten in a linear matrix form with respect to the inertial parameters of the mechanism, then parameters are grouped to obtain a set of independent base parameters, reducing the number of inertial parameters from 40 to 19. As a result, while maintaining the accuracy, the computational time is reduced to 63% of that of the original dynamic model. Finally, to calibrate the dynamic model, an experimental dynamic identification is performed.

A general 5R spherical parallel manipulator.
The TezGoz spherical parallel manipulator 
Kinematic and Dynamic Analysis of a 3DOF Translational Parallel Manipulator
People Involved 
and Alaleh Arian

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 overconstraint three translational degreeoffreedom parallel manipulator. Since dynamic formulation of overconstraint 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 endeffector 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.
Freebody diagram of the Tripteron manipulator 
Singularityfree workspace of PMs using interval analysis and geometrical approach
People Involved 
and Stephane Caro

The presence of the singular configuration in the workspace of the parallel robots is a major deterrent to widespread of PMs in the industrial context. Therefore, these configurations must be avoided. There are many techniques addressed in the literature in order to obtain and avoid the singularity. Many of these techniques are applicable only in specific cases. In this project first, a novel approach is proposed to obtain the singularity expression of parallel robots using screw theory and geometric properties of singular configurations. Then, resorting to interval analysis, the branch and prune algorithm to obtain the workspace of robots is represented. A novel approach to obtain the maximal singularityfree circle/sphere in the workspace of planar PMs, such as 3RPR, and spatial PMs, such as 6UPS. The singularityfree workspace insures the application of the robot in aforementioned workspace.


Collisionfree Workspace of Parallel Mechanisms Using Interval Analysis
People Involved 
, Stephane Caro

This project proposes an intervalbased approach, to obtain the collisionfree workspace of planar parallel mechanisms. This approach is represented through an example for a 3RPR planar parallel mechanism and 6UPS spatial parallel mechanisms. Three main feature of the collisionfree workspace is taken into account: mechanical stroke of actuators, interference of limbs with the obstacle and interference of endeffector with the obstacle. In this project, a circle shaped obstacle is considered and its mechanical interference with limbs and edges of the endeffector is taken into account.


A Geometric Constructive Approach for Singularityfree Workspace of PMs
People Involved 
and Stephane Caro

This project proposes a novel approach to obtain the maximal singularityfree regions of planar parallel mechanisms which is based on a constructive geometric reasoning. The proposed approach consists of two algorithms. First, the borders of the singularityfree region corresponding to an arbitrary start point of the moving platform is obtained. Then, the second algorithm aims to find the center of the maximal singularityfree circle which is obtained using the socalled offset curve algorithm. As a case study, the procedure is applied to a 3PRR planar parallel mechanism and results are given in order to graphically illustrate the effectiveness of the proposed algorithm. The proposed approach can be directly applied to obtain the maximal singularityfree circle of similar parallel mechanisms, which is not the case for other approaches proposed in the literature which is limited to a given parallel mechanism, namely, 3RPR. Moreover, as the main feature of the proposed approach, it can be implemented both in a CAD system or in a computer algebra system where nonconvex and reentrant curves can be considered.


Workspace Determination of PMs with Progressive Growing Neural Gas Network (PGNGN)
People Involved 
,

In the most of the works for implementation and control of parallel robots, especially Generally, in parallel robots, solving the forward kinematic problem is much harder than finding the inverse kinematic solution, thus, workspace determination using FKP is a demanding task in most cases. Therefore, in this research, a progressive growing neural gas network algorithm (PGNGN) is proposed, which is a systematic and general approach to obtain the topology of the workspace based on IKP equations.
After establishing a preliminary network with few initial data points, the network starts to develop itself by considering new data points around its border neurons through a boundary data generation procedure. The proposed algorithm is able to continue learning, adding units and connections, until a performance criterion has been met which leads to a clear workspace topology with minimal errors.
The most important features of this algorithm are the abilities to detect cavities in the workspace, consider singularities and distinguish separated regions of the workspace. Till now, workspace of various parallel robots including 3RRR, 3RPR and 3PRR mechanisms and a GouphStewart platform have been determined. Results reveal the applicability and reliability of this method.
Then upon apply different levels of input voltage on the actuator, different step responses are studied in the presence of dead zone, delay and saturation. Through a linear identification process, a nominal secondorder linear model is estimated for the actuator. Based on the identified model, the position (length) of the actuator is controlled by applying some straightforward and reliable control solutions.


Workspace Determination of a 3DOF Parallel Robot Considering Joint Limits
People Involved 
,

Workspace analysis is one of the most important steps in the procedure of designing industrial robots. The workspace of a robot is defined as the set of all endeffector configurations which can be reached by some choice of joint coordinates.
Various approaches may be used to calculate the workspace of a parallel robot which can be classified by geometrical approaches, discretization method and numerical procedures.
The main features of the geometrical approaches are their fastness and accuracy, which are necessary in efficient calculation of some characteristics of the workspace, such as volume. Moreover, all mechanical and kinematic constraints can be considered using this method.
Using SolidWorks software, the workspace of a 3DOF decoupled parallel robot, developed in TaarLab, is determined, considering all joint limits and mechanical interface of joints. Since all DOFs are transitional the resulting area is an appropriate representation of the workspace.


Design, Development and Dynamic Simulation of a 2DOF Spherical PM
People Involved 
, , , Esmaeil Rostami

Spherical manipulators is a class of manipulators that can orient the endeffector about the center of rotation of the mechanism. The developed mechanism in this project performs as same as a human eye with a larger workspace. This mechanism can be employed in position tracking systems, such as object tracking cameras and antenna or solar tracker systems.
This mechanism benefits from two AX12 Dynamixel actuators which are both fixed to the base. All arms of the robot are designed in order to minimize the moving inertia of the mechanism to increase its agility. In each Rjoint, four SKF618 series bearings are used to ensure the alignment and sufficient stiffness of the joints. Recently, a wireless camera installed in the center of the endeffector is replaced with a higher fps PS4 camera to enhance the tracking performance of the robot.
The dynamic analysis used in this project is based on a judicious concept in detaching the whole mechanism into several subsystems and consecutive synergies between kinematic analysis, Lagrangian and Newtonian approaches. The proposed approach performance for the dynamics of this mechanism is analyzed by means of several test trajectories for the endeffector and the results are put into contrast by the ones obtained with a dynamic analyzer software. Then, a cosimulation between MATLAB and MDAdams has been accomplished in order to control this mechanism via computed torque method. The latter method has led the endeffector to follow the desired trajectory.
Finally, it should be noted that all image processing and object tracking codes are generated in C++ developed by QT Creator IDE by other members of the project.


Design, Development and Dynamic Simulation of a 3DOF Spherical PM
People Involved 
, , Milad Hasanvand

Spherical parallel manipulators have great advantages in their agility and stiffness. In this project, a 3DOF spherical parallel manipulator is designed based on Agile Eye 3DOF from Laval University. In TaarLab version, each Rjoint contains four SKF618 series bearings to ensure the alignment and sufficient stiffness of the joints.
Three Dynamixel actuators from MX series with good force control performance are used in order to use this robot in haptic applications like Lasik surgery on eyes and virtual dentistry training. Another main application of this spherical manipulator is in position tracking systems as previously mentioned about the 2DOF one.
The dynamic modeling approach used in this project is based on detaching the manipulator into several subsystems and applying a consecutive synergy between kinematic analysis, Lagrangian and Newtonian approaches. In this regard, the manipulator under study is detached to four subsystems. After writing down the kinematic equations of all the three subsystems, the Lagrangian and Newtonian approaches are blended and finally the dynamic model of the manipulator is obtained. Finally, the problem leads to a system of 12 equations and 18 unknowns, which has been simplified to have a fully constraint system of equations. The results are put into contrast by the one obtained with an analyzer software, MDAdams. Then, a cosimulation between MATLAB and MDAdams has been accomplished in order to control the manipulator with computed torque control method. The latter method has led to the endeffector to follow the desired trajectory perfectly.


Design, Development and Dynamic Simulation of Triptron
People Involved 
, , ,

Parallel manipulators play a very important role in pick and place tasks in robotic industries due to their precision and high velocities. In this project which is funded by the INSF, a new configuration of Tripteron which is a 3DOF fullydecoupled firstly built in Laval University is developed in order to increase its workspace and acceleration.
The manipulator contains three PRRR structure limbs with fixedbase actuators. This let us use powerful 1.2 KW BONMET AC Servo actuators with great control performance. All moving parts are made of AL 7075T6 alloy to increase the stiffness and reduce the moving inertia of the mechanism and precise linear modules are used as active the prismatic joints.
Based on the application, various tools or parts could be attached to the endeffector of the manipulator such as a pneumatic gripper. Due to the high acceleration of the manipulator, it also could be used as a test platform to do functional test of product in high acceleration. Moreover, since the actuator perform well in force feedback control, this mechanism also could be used as a haptic rehabilitation system. The reasoning used in dynamic modeling of the manipulator is based on a judicious concept in detaching the whole mechanism into several subsystems and consecutive synergies between kinematic analysis, Lagrangian and Newtonian approaches.


Design and Development of a Pneumatic 6DOF GoughStewart
People Involved 
, Milad Hasanvand, , Foad Saniei

This robot is developed in order to have an experimental platform to simulate 6DOF motions of dynamic systems such as driving and flight simulators.
Developed platform has six links and each link contains one linear potentiometer, for the exact position of link, two pressure indicators, for input and output pressures of the jack, and one valve to adjust the air flow. These actuators were connected to the base with spherical or universal joints. The orientation and position of the moving platform are given and using Inverse Kinematic Problem (IKP) trying to obtain the length of each link. Then air flow rate of each valve and rate of air pressure passing over each cylinder have been modeled based on displacement of each piston.
The reason for using GoughStewart platform as a flight simulator is mainly due to its high capability of load transferring. Moreover, high precision positioning is another advantage. Actuators are commonly under tension or compression forces rather than bending which results less deformation in them. In the most of the works for implementation and control of parallel robots, especially GoughStewart platform utilize electrical servo motors or force sensor and less attention has been paid to pneumatic actuators. Pneumatic actuators are favored because they have low weight, small size, high load operation and the possibility to use directly. Moreover, their cost is up to 20 percent less than electrical actuators and operating frequency is considerably higher than hydraulic actuators. High working range is another reason for using this type of actuators.


Design of 3RRR Planar PM for Object Tracking
People Involved 

This manipulator contains three RRR limb actuated with three AX23 Dynamixel motors fixed on the base. Similar to other manipulator designed in TaarLab, each Rjoint includes four bearing to ensure the alignment and sufficient stiffness and all moving parts are made of AL 7075T6 to minimize the moving inertia of the mechanism. This mechanism could be used in object tracking application by installing a camera on its endeffector. By adding other parts to the specified places on its base, the manipulator could be used either in horizontal or vertical position.


Design, Model & Control of a 3 DOF PM for Humanoid Neck Motion Simulator
People Involved 
, ,

Human neck has a complex musculoskeletal structure with seven vertebrae and more than twenty muscles. One of the main functions of neck is controlling head movements. These movements are: head pan, head tilt and head swing. We are interested in simulating neck movements, via parallel manipulators. In this project we are hoping to achieve two main goals:
1. Designing, Modeling and Optimizing: First stage of the research is to design a manipulator which provides three rotational degree of freedom about a fixed point with acceptable workspace and stiffness and realistic motion speed. We use optimization methods mostly convex optimization to achieve these prospects.
2. Controlling and Human Interaction: As the second part of the project we are interested in controlling the robot with brain signals extracted from an external headset, placed on users head. This part of the project involves fuzzy control and signal processing operations.
Results of this project can be used to help a person with neck movement problems, to control his/her head by just thinking about a desired movement!


Kinematic Optimization and Dimensional Synthesis of Parallel Robots
People Involved 

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 singularityfree 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 singularityfree 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.


Design, Development and Control of 3RRR Planar Parallel Mechanism
People Involved 
, ,

The 3RRR 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 endeffector, all the foregoing control approaches could be regarded as openloop control. In order to control the mechanism, two main control methods are used namely, position control and speed control. A Joystick 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 offline control, in which, the mechanism will follow a specific path defined in the program. In the second state, offline control via Joystick, the mechanism will follow a path specified by the user via Joystick. As the third state, which is considered as the online control via Joystick, the mechanism will interactively follow a path specified by the user via the Joystick. 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.


CollisionFree Workspac of Parallel Robots based on Convex Optimization Approach
People Involved 
Golnoush Asaeikheybari 
Parallel robots play a vital role in today’s industry. The analysis of Kinematics, workspace and singularities of the proposed robots is of considerable complexity. The main contribution of this research is exerting analytical methods based on convex optimization to tackle the problems that arouse due to singularity. To reach this goal, the largest singularity free convex ellipsoid in the workspace of the proposed parallel robots will be extracted. To this purpose, new convexoptimization based algorithms will be introduced for 3DOFs and 4DOFs Delta and 3UPU parallel robots. Mathematical knowledge in the fields of linear algebra and matrix analysis, convex optimization, algebraic geometry, and etc. is prerequisite for the analysis of the aforementioned purposes.

