Transactions of the Canadian Society for Mechanical Engineering
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Volume 35 (2011), Issue 4
M. John D. Hayes, Roger Boudreau
Geometric analysis of the kinematic sensitivity of planarparallel mechanisms
Mohammad Hossein Saadatzi, Mehdi Tale Masouleh, Hamid D. Taghirad, Cl閙ent Gosselin, Philippe Cardou
The kinematic sensitivity is a unit-consistent measure that has been recently proposed as a mechanism performance index to compare robot architectures. This paper presents a robust geometric approach for computing this index for the case of planar parallel mechanisms. The physical meaning of the kinematic sensitivity is investigated through different combinations of the Euclidean and infinity norms and by means of several illustrative examples. Finally, this paper opens some avenues to the dimensional synthesis of parallel mechanisms by exploring the meaning of the global kinematic sensitivity index.
The dynamics of a single algebraic screw pair
James D. Robinson, M. John D. Hayes
The algebraic screw pair, or A-pair, represents a new class of kinematic constraint that exploits the self-motions inherent to a specific configuration of Griffis-Duffy platform. Using the A-pair as a joint in a hybrid parallel-serial kinematic chain results in a sinusoidal coupling of rotation and translation between adjacent links. The resulting linkage is termed an A-chain. This paper reveals the dynamic equations of motion of a single A-pair and examines the impact of the inertial properties of the legs of the A-pair on the dynamics. A numerical example illustrates the impact of the leg effects from different perspectives and shows that while the gravity effects of the legs are significant, it may be possible to neglect the leg kinetic energy from the dynamics model.
Length-optimized smooth obstacle avoidance for robotic manipulators
Soheil S. Parsa, Juan A. Carretero, Roger Boudreau
This paper presents a novel optimized smooth obstacle avoidance algorithm for robotic manipulators. First, a 3𣯗 interpolating polynomial is used to plan a smooth trajectory between initial and final positions in the joint space without considering any obstacles. Then, a simple harmonic function, which is smooth and continuous in displacement, velocity and acceleration, is applied to generate a new smooth path avoiding collisions between the robot links and an obstacle. The obstacle avoidance portions on the path are optimized such that the length of the path traversed by the end-effector is minimized. Simulation results for a 6 DOF serial manipulator demonstrate the efficiency of the proposed method.
Singularity analysis of the 4 RUU parallel manipulator using Grassmann-Cayley algebra
Semaan Amine, Mehdi Tale Masouleh, St閜hane Caro, Philippe Wenger, Cl閙ent Gosselin
This paper deals with the singularity analysis of four degrees of freedom parallel manipulators with identical limb structures performing Sch鰊flies motions, namely, three independent translations and one rotation about an axis of fixed direction. The 6×6 Jacobian matrix of such manipulators contains two lines at infinity among its six Pl點ker vectors. Some points at infinity are thus introduced to formulate the superbracket of Grassmann-Cayley algebra, which corresponds to the determinant of the Jacobian matrix. By exploring this superbracket, all the singularity conditions of such manipulators can be enumerated. The study is illustrated through the singularity analysis of the 4-RUU parallel manipulator.
Lagrangian dynamics of cable-driven parallel manipulators: A variable mass formulation
Yousef B. Bedoustani, Pascal Bigras, Hamid D. Taghirad, Ilian A. Bonev
In this paper, dynamic analysis of cable-driven parallel manipulators (CDPMs) is performed using the Lagrangian variable mass formulation. This formulation is used to treat the effect of amass stream entering into the system caused by elongation of the cables. In this way, a complete dynamic model of the system is derived, while preserving the compact and tractable closed-form dynamics formulation. First, a general formulation for a CDPM is given, and the effect of change of mass in the cables is integrated into its dynamics. The significance of such a treatment is that a complete analysis of the dynamics of the system is achieved, including vibrations, stability, and any robust control synthesis of the manipulator. The formulation obtained is applied to a typical planar CDPM. Through numerical simulations, the validity and integrity of the formulations are verified, and the significance of the variable mass treatment in the analysis is examined. For this example, it is shown that the effect of introducing a mass stream into the system is not negligible. Moreover, it is non linear and strongly dependent on the geometric and inertial parameters of the robot, as well as the maneuvering trajectory.
Dynamic analysis and control of cable driven robots with elastic cables
Mohammad A. Khosravi, Hamid D. Taghirad
In this paper modeling and control of cable driven redundant parallel manipulators with flexible cables, are studied in detail. Based on new results, in fully constrained cable robots, cables can be modeled as axial linear springs. Considering this assumption the system dynamics formulation is developed using Lagrange approach. Since in this class of robots, all the cables should remain in tension for the whole workspace, the notion of internal forces are introduced and incorporated in the proposed control algorithm. The control algorithm is developed in cable coordinates in which the internal forces play an important role. Finally, asymptotic stability of the closed loop system is analyzed through Lyapunov theorem, and the performance of the proposed algorithm is studied by simulations.
Motion recovery after joint failure in parallel manipulators
In this paper, the failure of parallel manipulators is investigated. Failure modes of parallel manipulators and their causes and effects from the kinematics point of view are discussed. Methodologies for investigating the effect of failures, due to joint failure or singularity, on the motion performance of manipulators are presented, and the criteria for full and partial recovery from these failures are established. The proposed methodologies are based on the projection of the lost motion onto the orthogonal complement of the null space of the Jacobian matrix after failure. The procedure is simulated for planar parallel manipulators to examine if after joint failure the required motion of manipulator could be fully recovered; as well as to calculate the corrections to the motion of remaining joints for recovering the lost motion.
Kinematic analysis of a translational 3-DoF tensegrity mechanism
Chris A. Mohr, Marc Arsenault
This paper presents a novel three-degree-of-freedom mechanism based on a known tensegrity architecture. The mechanism is cable driven and shown to exhibit three-dimensional translational motion. Analytical solutions to the direct and inverse kinematic problems are produced based on the geometry and statics of the mechanism. The boundaries of the reachable Cartesian workspace are developed based on maintaining valid tensegrity configurations and requiring the actuated cables to be in tension. The low inertia, relatively large workspace volume and the movement produced by the mechanism make it promising for high speed applications such as pick and place operations.
Full journal title: Transactions of the Canadian Society for Mechanical Engineering
Abreviated journal title: Trans. Can. Soc. Mech. Eng.
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