Jeh Won Lee

Optimal torque distribution method for a redundantly actuated 3-RRR parallel robot using a geometrical approach

In this paper, a novel optimal torque distribution method for a redundantly actuated parallel robot is proposed. Geometric analysis based on screw theory is performed to calculate the stiffness matrix of a redundantly actuated 3-RRR parallel robot. The analysis is performed based on statics focusing on low-speed motions. The stiffness matrix consisting of passive and active stiffness is also derived by the differentiation of Jacobian matrix. Comparing two matrices, we found that null-space vector is related to link geometry. The optimal distribution torque is determined by adapting mean value of minimum and maximum angles as direction angles of null-space vector. The resulting algorithm is validated by comparing the new method with the minimum-norm method and the weighted pseudo-inverse method for two different paths and force conditions. The proposed torque distribution algorithm shows the characteristics of minimizing the maximum torque.

Kinematic Optimal Design on a New Robotic Platform for Stair Climbing

Stair climbing is one of critical issues for field robots to widen applicable areas. This paper presents optimal design on kinematic parameters of a new robotic platform for stair climbing. The robotic platform climbs various stairs by body-flip locomotion with caterpillar type main platform. Kinematic parameters such as platform length, platform height, and caterpillar rotation speed are optimized to maximize stair-climbing stability. Three types of stairs are used to simulate typical user conditions. The optimal design process is conducted based on Taguchi methodology, and resulting parameters with optimized objective function are presented. In near future, a prototype is assembled for real environment testing.

A geometric approach for singularity analysis of 3-DOF planar parallel manipulators using Grassmann–Cayley algebra

Singular configurations of parallel manipulators (PMs) are special poses in which the manipulators cannot maintain their inherent infinite rigidity. These configurations are very important because they prevent the manipulator from being controlled properly, or the manipulator could be damaged. A geometric approach is introduced to identify singular conditions of planar parallel manipulators (PPMs) in this paper. The approach is based on screw theory, Grassmann–Cayley Algebra (GCA), and the static Jacobian matrix. The static Jacobian can be obtained more easily than the kinematic ones in PPMs. The Jacobian is expressed and analyzed by the join and meet operations of GCA. The singular configurations can be divided into three classes. This approach is applied to ten types of common PPMs consisting of three identical legs with one actuated joint and two passive joints.

Stiffness synthesis of 3-DOF planar 3RPR parallel mechanisms

Force control is important in robotics research for safe operation in the interaction between a manipulator and a human operator. The elasticity center is a very important characteristic for controlling the force of a manipulator, because a force acting at the elasticity center results in a pure displacement of the end-effector in the same direction as the force. Similarly, a torque acting at the elasticity center results in a pure rotation of the end-effector in the same direction as the torque. A stiffness synthesis strategy is proposed for a desired elasticity center for three-degree-of-freedom (DOF) planar parallel mechanisms (PPM) consisting of three revolute-prismatic-revolute (3RPR) links. Based on stiffness analysis, the elasticity center is derived to have a diagonal stiffness matrix in an arbitrary configuration. The stiffness synthesis is defined to determine the configuration when the elasticity center and the diagonal matrix are given. The seven nonlinear system equations are solved based on one reference input. The existence and the solvability of the nonlinear system equations were analyzed using reduced Grobner bases. A numerical example is presented to validate the method.

Geometrical Kinematic Analysis of a Planar Serial Manipulator Using a Barycentric Formula

The kinematics, instantaneous motion, and statics of a manipulator have recently been determined algebraically. In the past, such studies did not provide any intuition about the equation. Robot designers had to use a numerical method or trial-and-error solver with unintuitive equations. Alternatively, all algebraic processes have their own geometrical meaning. Geometric analysis provides intuition for designing the linkages of a robot. Screw theory and barycentric formulas are used to find meaningful geometric measures. The kinematics and statics of a manipulator are described by an axis screw and its reciprocal line screw. The barycenter of a triangle with edges and a perpendicular distance between the two screws are useful geometric measures for geometric analysis. This study provides a geometric interpretation of the kinematics and statics of a planar manipulator using a barycentric formula.Copyright