Stefan Staicu

Inverse dynamics of the 3-PRR planar parallel robot

Recursive modelling for the kinematics and dynamics of the known 3-PRR planar parallel robot is established in this paper. Three identical planar legs connecting to the moving platform are located in a vertical plane. Knowing the motion of the platform, we develop first the inverse kinematics and determine the positions, velocities and accelerations of the robot. Further, the principle of virtual work is used in the inverse dynamics problem. Several matrix equations offer iterative expressions and graphs for the power requirement comparison of each of three actuators in two different actuation schemes: prismatic actuators and revolute actuators. For the same evolution of the moving platform in the vertical plane, the power distribution upon the three actuators depends on the actuating configuration, but the total power absorbed by the set of three actuators is the same, at any instant, for both driving systems. The study of the dynamics of the parallel mechanisms is done mainly to solve successfully the control of the motion of such robotic systems.

Dynamic modelling of a 3-DOF parallel manipulator using recursive matrix relations

In this paper, a simple and convenient method – Recursive Matrix method – is proposed for kinematic and dynamic analysis of all types of complex manipulators. After addressing the principle of the method, an example – a 3-DOF parallel manipulator with prismatic actuators – is demonstrated for the efficiency of the method in solving kinematic and dynamic problems of complex manipulators. With the inverse kinematic solutions, the inverse dynamic problem is solved with the virtual powers method. Matrix relations and graphs of the acting forces and powers for all actuators are analysis and determined. It is shown that the proposed method is an effective mean for kinematic and dynamic modelling of parallel mechanisms.

Recursive modelling in dynamics of delta parallel robot

Recursive matrix relations in kinematics and dynamics of a Delta parallel robot having three revolute actuators are established in this paper. The prototype of the manipulator is a three degrees-of-freedom space mechanism, which consists of a system of parallel closed kinematical chains connecting to the moving platform. Knowing the translation motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity and acceleration of each robots element. Further, the inverse dynamic problem is solved using an approach based on the fundamental principle of virtual work. Finally, a comparative study on time-history evolution of the torques of the three actuators is analysed.

Dynamics analysis of the Star parallel manipulator

Matrix relations in kinematics and dynamics of the Star parallel manipulator are established in this paper. The prototype of the manipulator is a three-degree-of-freedom mechanism, which consists of a system of parallel kinematical chains connecting to a moving platform. Knowing the translation motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity and acceleration of each robots link. Further, the inverse dynamics problem is solved using an approach based on the principle of virtual work, but it has been verified the results in the framework of the Lagrange equations with their multipliers. Recursive formulae offer expressions and graphs for the power requirement comparison of each of three actuators in two computational complexities: complete dynamic model and simplified dynamic model.

Planetary gear train for robotics

A recursive matrix model concerning the geometric analysis, kinematics and dynamics of a Bendix wrist planetary bevel-gear train for robotics is established in this paper. The prototype of this mechanism is a three-degree-of-freedom system with seven links and four bevel gear pairs. Controlled by electric motors, three active elements of the robot have three independent rotations. Supposing that the position and the rotational motion of the platform are known, an inverse dynamic problem is developed using the virtual power approach. Finally, some recursive matrix relations and some graphs for the torques of the actuators are determined.

Dynamics modelling of a Stewart-based hybrid parallel robot

Matrix relations for kinematics and dynamics analysis of a spatial two-module Stewart-based hybrid parallel robot are established in this paper. Knowing the relative motions of two moving platforms, the inverse dynamics problem is solved based on a set of recursive explicit equations. Finally, compact results and graphs of simulation for the input forces and powers of all actuators are obtained.

Dynamics of delta parallel robot with prismatic actuators

Recursive matrix relations for kinematics and dynamics of a new delta parallel robot with concurrent prismatic actuators are established in this paper. This parallel mechanism consists of several kinematical closed chains. The three active elements of the sliding manipulator, acted by some horizontal concurrent forces, which are generated by some hydraulic or pneumatic systems, have three independent translations. Knowing the translation motion of the platform, one initially develops the inverse kinematical problem and determines the positions, velocities and accelerations of the manipulator. Further, the virtual power principle is used in the inverse dynamic problem. Some matrix equations offer iterative expressions and graphs for the actuating forces and powers of the three actuators.

Inverse dynamics of star parallel manipulator

Recursive matrix relations for kinematics and dynamics of a Herves star parallel manipulator are established in this paper. The prototype of this robot is a three-degree of freedom spatial mechanism, which consists of a system of parallel kinematical chains. Supposing that the position and the translation motion of the platform are known, an inverse dynamic problem is solved using a new matrix approach. Finally, some iterative matrix relations and some graphs for the torques and the powers of the three active couples are determined.

Matrix modelling in dynamics of a 2-DOF orienting gear train

Recursive matrix relations for kinematics and dynamics analysis of a 2-DOF orienting gear train are established in this paper. The mechanism is a parallel system with five moving links and three bevel gear pairs controlled by two electric motors. Knowing the rotation motion of the end-effector, the inverse dynamic problem is solved using an approach based on the principle of virtual work and have verified the results in the framework of the Lagrange equations of the second kind. Finally, some graphs for the input angles of rotation, the forces and the powers of the actuators are obtained.

Fuzzy Thrust Staging Kinematics for the NERVA Strap-On Boosters

NERVA small space launcher under development in Romania by Politehnica University is based on the solution of hard take-off with three strep-on SRM boosters. Due to the very high thrust enhancement a lift-off loading of more than 40 g-s appears, which is quite challenging. The main challenge is connected with the possible uneven thrust and burn duration of the three SRE-s of the first stage, which we call fuzzy thrust. Experimental data show variations of up to 0.5 seconds in the duration of the powered phase of SRE-s, from a total of 3.0 seconds of a mean burn. Yet undetermined variations in the total ignition delay between individual motors are a stronger concern. While for the unique booster of the standard SA-2 vehicle the ignition delay has no impact, when those engines are forced to work in parallel the individual differences become catastrophic. Severe imbalance between the two lateral engines may occur, ending in a potentially severe damage of the launching rail, possible loss of flight stability along the boost phase and damage of the second stage structure. The problems regarding the efficiency of the propulsion system that accompany this project are considered and solutions are proposed for the high thrust augmentation of the booster stage. Cryogenic vs storable propellants are studied for thrust augmentation of the boosters.