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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.

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.