Non-singular assembly mode changing trajectories in the workspace for the 3-RPS parallel robot

Having non-singular assembly modes changing trajectories for the 3-RPS parallel robot is a well-known feature. The only known solution for defining such trajectory is to encircle a cusp point in the joint space. In this paper, the aspects and the characteristic surfaces are computed for each operation mode to define the uniqueness of the domains. Thus, we can easily see in the workspace that at least three assembly modes can be reached for each operation mode. To validate this property, the mathematical analysis of the determinant of the Jacobian is done. The image of these trajectories in the joint space is depicted with the curves associated with the cusp points

Uniqueness domains and non singular assembly mode changing trajectories

Parallel robots admit generally several solutions to the direct kinematics problem. The aspects are associated with the maximal singularity free domains without any singular configurations. Inside these regions, some trajectories are possible between two solutions of the direct kinematic problem without meeting any type of singularity: non-singular assembly mode trajectories. An established condition for such trajectories is to have cusp points inside the joint space that must be encircled. This paper presents an approach based on the notion of uniqueness domains to explain this behaviour

Working and Assembly Modes of the Agile Eye

This paper deals with the in-depth kinematic analysis of a special spherical parallel wrist, called the Agile Eye. The Agile Eye is a three-legged spherical parallel robot with revolute joints in which all pairs of adjacent joint axes are orthogonal. Its most peculiar feature, demonstrated in this paper for the first time, is that its (orientation) workspace is unlimited and flawed only by six singularity curves (rather than surfaces). Furthermore, these curves correspond to self-motions of the mobile platform. This paper also demonstrates that, unlike for any other such complex spatial robots, the four solutions to the direct kinematics of the Agile Eye (assembly modes) have a simple geometric relationship with the eight solutions to the inverse kinematics (working modes)

Inverse Dynamics of a Redundantly Actuated Four-Bar Mechanism Using an Optimal Control Formulation

This paper presents an approach to estimating joint torques in a four-bar closed-chain mechanism with prescribed kinematics and redundant actuation, i.e., with more actuators than degrees of freedom. This problem has several applications in industrial robots, machine tools, and biomechanics. The inverse dynamics problem is formulated as an optimal control problem (OCP). The dynamical equations are derived for an open-chain mechanism, what keeps the formulation simple and straightforward. Sets of constraints are explored to force the three-link open-chain to behave as a four-bar mechanism with a crank rotating at a constant velocity. The controls calculated from the OCP are assumed to be the input joint torques. The standard case with one torque actuator is solved and compared to cases with two and three actuators. The case of two actuators presented the smallest peak and mean torques, using one specific set of constraints. Such torques were smaller than the solution obtained using an alternative method existing in literature that solves the redundancy problem by means of the pseudo-inverse matrix. Comparison with inverse dynamics solutions using well-established methods for the one-actuator closedloop four-bar were equal. Reconstructed kinematical trajectories from forward integration of the closed-loop mechanism with the OCP obtained torques were essentially similar. The results suggest that the adopted procedure is promising, giving solutions with lower torque requirements than the regularly actuated case and redundantly actuated computed with other approaches. The applicability of the method has been shown for the four-bar mechanism. Other classes of redundantly actuated, closed-loop mechanisms could be tested using a similar formulation. However, the numerical parameters of the OCP must be chosen carefully to achieve convergence

Optimisation of controlled motion of closed-loop chain manipulator robots with different degree and type of actuation

A number of energy-optimal control problems for a new structure of closed-loop manipulator robot are considered. We present methodology and algorithm that is suitable for solving optimization problems for manipulator robots with different degree and type of actuation. This methodology isbased on polynomial and Fourier series approximation of independently varying functions and conversion of the initial optimal control problem into the constrained parameter optimization problem. The methodology has been successfully used for optimization of under-, fully-, and overactuated robots having both external (powered) drives and internal (unpowered or passive) spring-damper-like drives. Comparison analysis of the simulation results of the obtained energy-optimal control processes fordifferent manipulator robots is presented

Static force capabilities and dynamic capabilities of parallel mechanisms equipped with safety clutches

Cette thèse étudie les forces potentielles des mécanismes parallèles plans à deux degrés de liberté équipés d'embrayages de sécurité (limiteur de couple). Les forces potentielles sont étudiées sur la base des matrices jacobienne. La force maximale qui peut être appliquée à l'effecteur en fonction des limiteurs de couple ainsi que la force maximale isotrope sont déterminées. Le rapport entre ces deux forces est appelé l'efficacité de la force et peut être considéré ; comme un indice de performance. Enfin, les résultats numériques proposés donnent un aperçu sur la conception de robots coopératifs reposant sur des architectures parallèles. En isolant chaque lien, les modèles dynamiques approximatifs sont obtenus à partir de l'approche Newton-Euler et des équations de Lagrange pour du tripteron et du quadrupteron. La plage de l'accélération de l'effecteur et de la force externe autorisée peut être trouvée pour une plage donnée de forces d'actionnement.This thesis investigates the force capabilities of two-degree-of-freedom planar parallel mechanisms that are equipped with safety clutches (torque limiters). The force capabilities are studied based on the Jacobian matrices. The maximum force that can be applied at the end-effector for given torque limits (safety index) is determined together with the maximum isotropic force that can be produced. The ratio between these two forces, referred to as the force effectiveness, can be considered as a performance index. Finally, some numerical results are proposed which can provide insight into the design of cooperation robots based on parallel architectures. Considering each link and slider system as a single body, approximate dynamic models are derived based on the Newton-Euler approach and Lagrange equations for the tripteron and the quadrupteron. The acceleration range or the external force range of the end-effector are determined and given as a safety consideration with the dynamic models