| This dissertation deals with a general kinematic synthesis method for “Discretely Actuated Robotic Manipulators”, or “D-ARMs”. A D-ARM is any member of a class of robotic manipulators powered by actuators which have only discrete positional stable states, e.g., solenoids or pneumatic cylinders without feedback control. The categorization of D-ARM should be recognized as an extension of the “Binary arm” concept introduced by Chirikjian.; The main kinematic synthesis problem proposed in this dissertation is: “Given a D-ARM and finite sets of desired positions and orientations of a D-ARM's end-effector (desired frames), determine the kinematic parameters of the manipulator”. It is a key issue of this dissertation that the desired end-effector orientations in 3D space as well as the desired positions must be dealt with.; The proposed conceptual framework of a general synthesis method to solve this main problem is based on an incremental synthesis with a numerically obtained Jacobian matrix of a given manipulator and its generalized inverse matrix.; Simulations are conducted to demonstrate the feasibility of the main synthesis method. Through the simulations, it is shown that the method is applicable to a wide variety of scenarios, such as 2D/3D workspaces, Serial/Parallel/Hybrid arm architectures, and Sufficient/Insufficient/Redundant kinematic cases. It is also shown that the computation time is short enough to design a real D-ARM even in a PC environment, and that the numerical errors are small from the viewpoint of dimensional accuracy of mechanical parts.; Besides the main problem, two other synthesis problems are also discussed. The proposed sub-problems are concerned with optimal pose and actuator placement for D-ARMs to reach specified frames. These problems can be viewed as pre-processing steps that condition the baseline design so that it need not be altered so much in order to meet the design criteria. Several approaches are presented to solve these sub-problems. The concept of a gradient on the Special Euclidean group, SE(3) is utilized to formulate these approaches. |
