Inverse and forward kinematics and workspace analysis of a novel 5-DOF (3T2R) parallel–serial (hybrid) manipulator:

The proposed study provides a solution of the inverse and forward kinematic problems and workspace analysis for a five-degree-of-freedom parallel–serial manipulator, in which the parallel kinematic chain is made in the form of a tripod and the serial kinematic chain is made in the form of two carriages displaced in perpendicular directions. The proposed manipulator allows to realize five independent movements—three translations and two rotations motion pattern (3T2R). Analytical relationships between the coordinates of the end-effector and five controlled movements provided by manipulator's drives (generalized coordinates) were determined. The approach of reachable workspace calculation was defined with respect to available design constraints of the manipulator based on the obtained algorithms of the inverse and forward kinematics. Case studies are considered based on the obtained algorithms of inverse and forward kinematics. For the inverse kinematic problem, the solution is obtained in accordance with the given laws of position and orientation change of the end-effector, corresponding to the motion along a spiral-helical trajectory. For the forward kinematic problem, various assemblies of the manipulator are obtained at the same given values of the generalized coordinates. An example of reachable workspace designing finalizes the proposed study. Dimensions and extreme values of the end-effector orientation angles are calculated

Kinematics and workspace analysis of a 3ppps parallel robot with u-shaped base

This paper presents the kinematic analysis of the 3-PPPS parallel robot with an equilateral mobile platform and a U-shape base. The proposed design and appropriate selection of parameters allow to formulate simpler direct and inverse kinematics for the manipulator under study. The parallel singularities associated with the manipulator depend only on the orientation of the end-effector, and thus depend only on the orientation of the end effector. The quaternion parameters are used to represent the aspects, i.e. the singularity free regions of the workspace. A cylindrical algebraic decomposition is used to characterize the workspace and joint space with a low number of cells. The dis-criminant variety is obtained to describe the boundaries of each cell. With these simplifications, the 3-PPPS parallel robot with proposed design can be claimed as the simplest 6 DOF robot, which further makes it useful for the industrial applications

Workspace and Kinematic Analysis of the VERNE machine

This paper describes the workspace and the inverse and direct kinematic analysis of the VERNE machine, a serial/parallel 5-axis machine tool designed by Fatronik for IRCCyN. This machine is composed of a three-degree-of-freedom (DOF) parallel module and a two-DOF serial tilting table. The parallel module consists of a moving platform that is connected to a fixed base by three non-identical legs. This feature involves (i) a simultaneous combination of rotation and translation for the moving platform, which is balanced by the tilting table and (ii) workspace whose shape and volume vary as a function of the tool length. This paper summarizes results obtained in the context of the European projects NEXT ("Next Generation of Productions Systems")

Kinematic and Dynamic Analysis of the 2-DOF Spherical Wrist of Orthoglide 5-axis

This paper deals with the kinematics and dynamics of a two degree of freedom spherical manipulator, the wrist of Orthoglide 5-axis. The latter is a parallel kinematics machine composed of two manipulators: i) the Orthoglide 3-axis; a three-dof translational parallel manipulator that belongs to the family of Delta robots, and ii) the Agile eye; a two-dof parallel spherical wrist. The geometric and inertial parameters used in the model are determined by means of a CAD software. The performance of the spherical wrist is emphasized by means of several test trajectories. The effects of machining and/or cutting forces and the length of the cutting tool on the dynamic performance of the wrist are also analyzed. Finally, a preliminary selection of the motors is proposed from the velocities and torques required by the actuators to carry out the test trajectories

A hyper-redundant manipulator

“Hyper-redundant” manipulators have a very large number of actuatable degrees of freedom. The benefits of hyper-redundant robots include the ability to avoid obstacles, increased robustness with respect to mechanical failure, and the ability to perform new forms of robot locomotion and grasping. The authors examine hyper-redundant manipulator design criteria and the physical implementation of one particular design: a variable geometry truss

Analysis of a closed-kinematic chain robot manipulator

Presented are the research results from the research grant entitled: Active Control of Robot Manipulators, sponsored by the Goddard Space Flight Center (NASA) under grant number NAG-780. This report considers a class of robot manipulators based on the closed-kinematic chain mechanism (CKCM). This type of robot manipulators mainly consists of two platforms, one is stationary and the other moving, and they are coupled together through a number of in-parallel actuators. Using spatial geometry and homogeneous transformation, a closed-form solution is derived for the inverse kinematic problem of the six-degree-of-freedom manipulator, built to study robotic assembly in space. Iterative Newton Raphson method is employed to solve the forward kinematic problem. Finally, the equations of motion of the above manipulators are obtained by employing the Lagrangian method. Study of the manipulator dynamics is performed using computer simulation whose results show that the robot actuating forces are strongly dependent on the mass and centroid locations of the robot links