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1.1 Problem definition 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 (Nof, 1999). Several researchers have investigated workspace boundaries for different degrees of freedom (DOF), joint types and kinematic structures utilizing many approaches (Ceccarelli , 1996), (Ceccarelli & Vinciguerra, 1995), (Ceccarelli & Lanni, 2004), (Cebula & Zsombor-Murray, 2006), (Castelli, et al., 2008), (Yang, et al., 2008). A recent example utilizes a reconfigurable modeling approach, where the 2D and 3D boundary workspace is created by using a method identified as the Filtering Boundary Points (FBP) algorithm. This is developed fully in Djuric and ElMaraghy (2008). However, this work envelope based work is limited as it does not contain relevant information regarding the relationships between the robot, or mechanisms within a system. This includes the general kinematic structures within the system, the location of the working part(s), tools, process parameters and other operation related parameters. Here an operation is defined as consisting of the travel path, manipulator/end-effector or working tool, tool and part location, and orientation, and any other related process related parameters. 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 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, reconfigurable machines, and manufacturing cells. Multi-tasking machine tools can be considered CNC mill-lathe hybrids (Figure 1). These machines enable multiple tool engagement in multiple parts simultaneously. Each tool/ part/ spindle/ axis set combination follows its own unique programmed path. These machines minimize the number of manual operations, as well as reduce setup costs and potential quality issues. A single multi-tasking machine tool can completely machine complex parts from start to finish (Hedrick & Urbanic, 2004). Traditional computer numerical control (CNC) machines consist of multiple kinematic chains (two – one to

Utilizing the Functional Work Space Evaluation Tool for Assessing a System Design and Reconfiguration Alternatives