Kinematic and Elastostatic Design Optimisation of the 3-DOF Gantry-Tau Parallel Kinematic Manipulator

Abstract

One of the main advantages of the Gantry-Tau machine is a large accessible workspace/footprint ratio compared to many other parallel machines. The Gantry-Tau improves this ration further by allowing a change of assembly mode without internal link collisions or collisions between the links and end-effector. The reconfigurable Gantry-Tau kinematic design obtained by multi-objective optimisation according to this paper gives the following features: 3-D workspace/footprint ratio is more than 3.19, lowest Cartesian stiffness in the workspace is 5N/µm and no link collisions detected. The optimisation parameters are the support frame lengths, the actuator positions and the robot's arm lengths. The results comparison between the evolutionary complex search algorithm and gradient-based method used for the Gantry-Tau design in the past is also presented in this paper. The detailed statics model analysis of the Gantry-Tau based on a functionally dependency is presented in this paper for the first time. Both the statics model and complex search algorithm may be applied for other 3-DOF Hexapods without major changes. The existing lab prototype of the Gantry-Tau was assembled and completed at the University of Agder, Norway.

Multicopter Design Optimization and Validation

“…Examples are Newton-Raphson gradient search methods and evolutionary-based search methods, such as the Complex method, see for example Whitney (1969) and Tyapin and Hovland (2009) where the optimization algorithm took several hours to converge towards an acceptable but sub-optimal solution. A linear program (LP) on the other hand, using the interior point method, can be solved in polynomial time, see Karmarkar (1984).…”

CAD-based approach for identification of elasto-static parameters of robotic manipulators

“…This motivates using advanced kinematical architectures (Orthoglide, Delta, Gantry-Tau, etc.) and light-weight materials, as well as minimization of the cross-sections of all manipulator elements [1][2][3][4]. The primary constraint for such minimization is the mechanical stiffness of the manipulator, which is directly related with the robot accuracy defined by the design specifications.…”

On the Stiffness Analysis and Elastodynamics of Parallel Kinematic Machines

“…Here, we choose to minimize V b w. r. t. θ, as for the case a), and u 1 2 .T h e reader should notice that our choice is not unique, it is only a particular reduction process necessary for our purposes, it means that the reader might develop a treatment in which u 1 2 is not dependent anymore. Now, by imposing that the derivative of V b w. r. t. θ vanishes, we obtain…”