Date of Award

Fall 11-2014

Document Type


Degree Name

Master of Science in Mechanical Engineering (MSME)


Mechanical Engineering

First Advisor

David Fisher

Second Advisor

Jerry Fine

Third Advisor

Carlotta Berry


One of the most important traits of a robotic manipulator is its work envelope, the space in which the robot can position its end effector. Parallel manipulators, while generally faster, are restricted by smaller work envelopes [1]. As such, understanding the parameters defining a physical robot’s work envelope is essential to the optimal design, selection, and use of robotic parallel manipulators. A Linear Delta Robot (LDR) is a type of parallel manipulator in which three prismatic joints move separate arms which connect to a single triangular end plate [2]. In this study, general inverse kinematics were derived for a linear delta robot. These kinematics were then used to determine the reachable points within a plane in the robot’s work envelope, incorporating the physical constraints imposed by a real robot. After simulating several robots of varying parameters, a linear regression was performed in order to relate the robot’s physical parameters to the inscribed radius of the area reachable in a plane of the LDR’s work envelope. Finally, a physical robot was constructed and used as a reality check to confirm the kinematics and inscribed radius. This study demonstrates the relationship between the LDR’s physical dimensions and the inscribed radius of its work envelope. Building a physical robot allowed confirmation of the resulting equation, validating an accurate representation of the LDR’s physical constraints. By doing so, the resulting equation provides a powerful tool for correctly sizing a LDR based on a desired work envelope.