An Automatic and General Approach to the Computational Analysis of Singular Configurations in Planar Mechanisms (original) (raw)
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Mechanism and Machine Theory, 2009
Singular configurations (singularities) are mechanism configurations where the instantaneous kinematics is locally undetermined. Since the indetermination of the instantaneous kinematics causes serious problems both to the static behavior and to the motion control of the mechanism, the research of all the singularities (singularity analysis) is a mandatory step during the design of mechanisms. This paper presents a new approach to implement the singularity analysis of planar mechanisms. The proposed technique extends the use of the instant center properties to the singularity analysis of planar mechanisms with more than one degree of freedom (dof). It exploits the results of previous works by the author in which a geometric and analytic technique has been presented to address the singularity analysis of single-dof planar mechanisms.
A novel geometric and analytic technique for the singularity analysis of one-dof planar mechanisms
Mechanism and Machine Theory, 2007
The importance of finding singular configurations (singularities) of mechanisms has become clear since the interest of the scientific community for parallel architectures arose. Regarding the singularity analysis, the main interest has been devoted to architectures with more-than-one degree of freedom (dof) without realizing that one-dof mechanisms are commonly used and deserve the same attention. This paper addresses the singularity analysis of one-dof planar mechanisms. A general method for implementing this analysis will be presented. The presented method relies on the possibility of giving geometric conditions for any type of singularity. It can be used to generate systems of equations to solve either for finding the singularities of a given mechanism or to synthesize mechanisms that have to match specific requirements about the singularities.
Analysis of configuration space singularities of closed-loop mechanisms and parallel manipulators
Mechanism and Machine Theory, 2004
A parallel manipulator or a closed-loop mechanism may gain or loose one or more degree-of-freedom at a singular point, and in this paper, we study the singularity associated with the gain of one or more degreesof-freedom. We analyze the constraint forces associated with the kinematic constraints inherent in a closedloop mechanism or a parallel manipulator, and characterize the gain singularities from the degeneracy of these constraint forces. Several special phenomena associated with gain singularity, such as locking of the actuators have been studied, and analytical criteria for these have been derived. We also present the necessary condition for finite self-motion and finite dwell of the passive links by analyzing second-order properties of the constraint equations. The results are illustrated with the help of several closed-loop mechanisms.
International Journal of Precision Engineering and Manufacturing, 2013
The singularity is a critical part of a parallel kinematic machine (PKM) in which the degree of freedom decreases or actuator forces conflict with one another to break down the PKM. Therefore, defining and avoiding the region of singularities are essential for safely operating PKMs. This paper proposes a new method for determining the singularity of a planar-type PKM with revolute joints by taking a geometric approach. The main idea of the paper is to use the wrench, not velocity, equation to calculate the Jacobian matrix. In addition, a distinct feature of the proposed method is that it uses perpendicular distances between end-effectors, actuators, and screws to determine singularities based on screw theory. This proposed method can analyze many types of PKMs, including nonredundant as well as redundant ones. The paper considers non-redundant and redundant 5-bar, 6-bar, 3-RRR, and 4-RRR PKMs for case studies. The proposed method is intuitive and simple and thus can be used for analyzing the singularity of various PKMs.
A practical procedure to analyze singular configurations in closed kinematic chains
IEEE Transactions on Robotics, 2004
The authors present a general method for the automated singularity analysis of any mechanism at a given configuration. The procedure uses a base of the motion space. This is obtained from a velocity equation characterized by a geometric matrix. This special form of Jacobian matrix has some advantages for automatic implementation. This approach provides the degree of freedom associated with the singularity, uncontrolled motion, and kinematic dependencies. It also facilitates the choice of actuators and redundant devices. The method has been implemented in a computer program for kinematic analysis.
A novel criterion for singularity analysis of parallel mechanisms
Mechanism and Machine Theory, 2019
A novel criterion for singularity analysis of parallel robots is presented. It relies on screw theory, the 3-dimensional Kennedy theorem, and the singular properties of minimal parallel robots. A parallel robot is minimal if in any generic configuration, activating any leg/limb causes a motion in all its joints and links. For any link of the robot, a pair of legs is removed. In the resulting 2 degrees-of-freedom mechanism, all possible instantaneous screw axes belong to a cylindroid. A center axis of this cylindroid is determined. This algorithm is performed for three different pairs of legs. The position is singular, if the instantaneous screw axis of the chosen link crosses and is perpendicular to three center axes of the cylindroids. This criterion is applied to a 6/6 Stewart Platform and validated on a 3/6 Stewart Platform using results known in the literature. It is also applied to two-platform minimal parallel robots and verified through the Jacobian; hence demonstrating its general applicability to minimal robots. Since any parallel robot is decomposable into minimal robots, the criterion applies to all constrained parallel mechanisms.
Singularity-locus expression of a class of parallel mechanisms
Robotica, 2002
In parallel mechanisms, singular configurations (singularities) have to be avoided during motion. All the singularities should be located in order to avoid them. Hence, relationships involving all the singular platform poses (singularity locus) and the mechanism geometric parameters are useful in the design of parallel mechanisms. This paper presents a new expression of the singularity condition of the most general mechanism (6-6 FPM) of a class of parallel mechanisms usually named fully-parallel mechanisms (FPM). The presented expression uses the mixed products of vectors that are easy to be identified on the mechanism. This approach will permit some singularities to be geometrically found. A procedure, based on this new expression, is provided to transform the singularity condition into a ninth-degree polynomial equation whose unknowns are the platform pose parameters. This singularity polynomial equation is cubic in the platform position parameters and a sixth-degree one in the p...
Singularity Analysis of Closed-loop Mechanisms and Parallel Manipulators
Singularity analysis is the study of gain or loss in degrees of freedom of a mechanism at a particular configuration. Singularity analysis is related to the degeneracy of Jacobian matrices relating configuration variables with task space variables. In this paper, we present an improved Jacobian formulation which can be used to identify not only the gain or loss of degrees of freedom, but, in addition, can be used to determine if the gain results in redundant degree of freedom. The approach and its advantages are illustrated with several examples.
Mechanism and Machine Theory, 2019
In the literature, velocity coefficients (VCs) and acceleration coefficients (ACs) were substantially proposed for single-degree-of-freedom (single-DOF) planar mechanisms. Their effectiveness in solving the kinematic analysis of these mechanisms is due to the fact that they only depend on the mechanism configuration. Such property also holds when they are defined for spatial single-DOF scleronomic and holonomic mechanisms, but was not exploited; moreover, some extensions of the VC and AC concepts to multi-DOF planar (or spatial scleronomic and holonomic) mechanisms are possible, but have not proved their practical usefulness. Here, first, the velocity-coefficient vectors (VCVs) together with their Jacobians (acceleration-coefficient Jacobians (ACJs) are proposed as an extension of the concepts of VC and AC to multi-DOF scleronomic and holonomic mechanisms. Then, a general algorithm, based on VCVs and ACJs and on a notation, previously presented by the author, which uses the complex-number method, is proposed for solving the kinematicanalysis problems of multi-DOF planar mechanisms and to find their links' dead-center positions. The effectiveness of the proposed algorithm is also illustrated by applying it to a case study. The proposed algorithm is efficient enough for constituting the kinematic block of any dynamic model of these mechanisms, and simple enough for being presented in graduate courses.
Journal of Mechanical Engineering, 2010
Instantaneous kinematics of a mechanism becomes undetermined when it is in a singular configuration; this indeterminacy has undesirable effects on static and motional behavior of the mechanism. So these configurations must be found and avoided during the design, trajectory planning and control stages of the mechanism. This paper presents a new geometrical method to find singularities of single-dof planar mechanisms using the concepts of mechanical advantage and instant centers.