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Path planning and re-planning for serial 6 degree of freedom (DOF) robotic systems is challenging due to complex kinematic structure and application conditions which affects the robot's tool frame position, orientation and singularity avoidance. These three characteristics represent the key elements for production planning and layout design of the automated manufacturing systems. The robot trajectory represents series of connected points in 3D space. Each point is defined with its position and orientation related to the robot's base frames or predefined user frame. The robot will move from point to point using the desired motion type (linear, arc, or joint). The trajectory planning requires first to check if robot can reach the selected part(s). This can be simply done by placing the part(s) inside the robot's work envelope. The robot's work envelope represents a set of all robots' reachable points without considering their orientation.

The ‘boundary of space’ model representing all possible positions which may be occupied by a mechanism during its normal range of motion (for all positions and orientations) is called the work envelope. In the robotic domain, it is also known as the robot operating envelope or workspace. Several researchers have investigated workspace boundaries for different degrees of freedom (DOF), joint types and kinematic structures utilizing many approaches. The work envelope provides essential boundary information, which is critical for safety and layout concerns, but the work envelope information does not by itself determine the reach feasibility of a desired configuration. The effect of orientation is not captured as well as the coupling related to operational parameters. Included in this are spatial occupancy concerns due to linking multiple kinematic chains, which is an issue with multi-tasking machine tools, and manufacturing cells.

When performing trajectory planning for robotic applications, there are many aspects to consider, such as the reach conditions, joint and end-effector velocities, accelerations and jerk conditions, etc. The reach conditions are dependent on the end-effector orientations and the robot kinematic structure. The reach condition feasibility is the first consideration to be addressed prior to optimizing a solution. The ‘functional’ work space or work window represents a region of feasible reach conditions, and is a sub-set of the work envelope. It is not intuitive to define. Consequently, 2D solution approaches are proposed. The 3D travel paths are decomposed to a 2D representation via radial projections. Forward kinematic representations are employed to define a 2D boundary curve for each desired end effector orientation.

A collaborative robot or cobot is a robot that can safely and effectively interact with human workers while performing industrial tasks. The ability to work alongside humans has increased the importance of collaborative robots in the automation industry, as this unique feature is a much needed property among robots nowadays. Rethink Robotics has pioneered this unique discipline by building many robots including the Baxter Robot which is exclusive not only because it has collaborative properties, but because it has two arms working together, each with 7 Degrees Of Freedom. The main goal of this research is to validate the kinematic equations for the Baxter collaborative robot and develop a unified reconfigurable kinematic model for the Left and Right arms so that the calculations can be simplified.

Inverse kinematic solutions of six degree of freedom (DOF) robot manipulation is a challenging task due to complex kinematic structure and application conditions which affects and depend on the robot’s tool frame position, orientation and different possible configurations. The robot trajectory represents a series of connected points in three dimensional space. Each point is defined with its position and orientation related to the robot’s base frames or users teach pendant. The robot will move from point to point using the desired motion type (linear, arc, or joint). This motion requires inverse kinematic solution. This paper presents a detailed inverse kinematic solution for Fanuc 6R (Rotational) robot family using a geometrical method. Each joint angular position will be geometrically analyzed and all possible solutions will be included in the decision equations. The solution will be developed in a parametric manner to cover the complete Fanuc six DOF family.

Gantry robots are mainly employed for applications requiring large workspace, with limited higher manipulability in one direction than the others. The Gantries offer very good mechanical stiffness and constant positioning accuracy, but low dexterity. Common gantries are CNC machines with three translational joints XYZ (3DOF) and usually with an attached wrist (+3DOF). The translational joints are used to move the tool in any position in the 3D workspace. The wrist is used to orient the tool by rotation about X, Y and Z axis. This standard kinematic structure (3T3R) produces a rectangular workspace. In this paper a full kinematic model for a 6DOF general CNC (gantry) machine is presented, along with the Jacobian matrix and singularity analysis. Using Denavit-Hartenberg convention, firstly, the general kinematic structure is presented, in order to assign frames at each link. The forward kinematic problem is solved using Maple 17 software.