An assertion that the parameters of a covariance structure are locally identified at a certain point only if the rank of the Jacobian matrix at that point equals the number of parameters, is shown to be false by means of a counterexample.

A novel couple-constrained parallel wrist with three measuring force flexible fingers is designed for grabbing heavy objects and measuring grabbed forces. Its prototype is developed, its dynamics model is established, and its grabbing forces are measured. First, using the extended formulas of the skew-symmetric matrix, the kinematic formulas are derived for solving the Jacobian/Hessian matrices and the general velocity/acceleration of the moving links in the couple-constrained parallel wrist. Second, a dynamics model is established for solving the dynamic actuation forces, the couple-constrained forces, and the torque in the couple-constrained parallel wrist. Third, the theoretical solutions of the kinematics/dynamics of the couple-constrained parallel wrist are verified using a simulation mechanism. Finally, the grabbing forces of the three flexible fingers are measured and analyzed.

Quantitative analysis of experimental metabolic data is frequently challenged by non-intuitive, complex patterns which emerge from regulatory networks. The complex output of metabolic regulation can be summarised by metabolic functions which comprise information about dynamics of metabolite concentrations. In a system of ordinary differential equations, metabolic functions reflect the sum of biochemical reactions which affect a metabolite concentration, and their integration over time reveals metabolite concentrations. Further, derivatives of metabolic functions provide essential information about system dynamics and elasticities. Here, invertase-driven sucrose hydrolysis was simulated in kinetic models on a cellular and subcellular level. Both Jacobian and Hessian matrices of metabolic functions were derived for quantitative analysis of kinetic regulation of sucrose metabolism. Model simulations suggest that transport of sucrose into the vacuole represents a central regulatory element in plant metabolism during cold acclimation which preserves control of metabolic functions and limits feedback-inhibition of cytosolic invertases by elevated hexose concentrations.

A mathematical method is developed to predict surge and instability inception in a centrifugal compressor map based on Greitzer and Moore model. The method uses phase plane and Jacobian matrix to determine stable and unstable zone of centrifugal compressor and to extract limit cycle in unstable zone. In order to evaluate accuracy of analytical method, a compressor test rig facility is designed and tested in order to be compared with theoretical results. Accurate Honeywell piezoelectric pressure transducers are used to measure time averaged pressure at inlet and outlet ducts of the compressor. In order to record the flow fluctuation precisely, hot wire sensors are installed in entrance and exit of impeller. The results represent instability inception near true stall point but different from measured data. The discrepancy mostly originates from inlet and outlet ducts which causes measure stall point of compressor deviates from true one. An analytical method which is able to predict surge and instability in a compressor is highly significant for instrumentation and controlling of system.

We present conditions for a set of matrices satisfying a permutation identity to be simultaneously triangularizable. As applications of our results, we generalize Radjavi’s result on triangularization of matrices with permutable trace and results by Yan and Tang on linear triangularization of polynomial maps.

This paper presents a novel reconfigurable parallel mechanism, which can serve as a machine tool. The proposed parallel mechanism can change its structure parameters by driving a bevel gear system fixed in the base platform. First, the forward and inverse kinematics of the proposed mechanism are investigated. Second, the reachable workspace and Jacobian matrix are conducted. Based on the Jacobian matrix, the stiffness model and dexterity of the end effector are developed in detail. Finally, a multi-objective optimization is performed by using the Genetic Algorithm, and the workspace and global performance indexes of stiffness as well as the dexterity are considered as the performance indices to improve the performance of the reconfigurable parallel mechanism. Finally, Pareto frontier figure and several tables are provided to illustrate the results of the optimization. The results showed the proposed method has improved the performance of the reconfigurable machine tool in terms of its stiffness and dexterity.

This paper proposes a systematic methodology to obtain a closed-form formulation for dynamics analysis of a novel spherical robot that is called a 3(RPSP)-S parallel manipulator. The proposed manipulator provides high rotational displacement of the moving platform for low angular displacement of the motors. The advised robot is suitable for repetitive oscillatory applications (for example, wrist and ankle rehabilitation and table of autopilot and gyroscope life test, etc.). First, we describe the structure of the proposed manipulator and solve the inverse kinematics problem of the manipulator. Next, based on the principle of virtual work, a methodology for deriving the dynamical equations of motion is developed. The elaborated approach shows that the inverse dynamics of the manipulator can be reduced to solving a system of three linear equations in three unknowns. Finally, a computational algorithm to solve the inverse dynamics of the manipulator is advised and several trajectories of the moving platform are simulated and verified by a special dynamics modeling commercial software (MSC ADAMS).

We present two methods to find all the possible conformations of short six degree-of-freedom segments of biopolymers which satisfy end constraints in position and orientation. One of our methods is motivated by inverse kinematic solution techniques which have been developed for “general” 6R serial robotic manipulators. However, conventional robot kinematics methods are not directly applicable to the geometry of polymers, which can be treated as a degenerate case where all the “link lengths” are zero. Here, we propose a method which extends the elimination method of Kohli and Osvatic. This method can be applied directly to the geometry of biopolymers. We also propose a heuristic method based on a Lie-group-theoretic description. In this method, we utilize inverse iterations of the Jacobian matrix to obtain all conformations which satisfy end constraints. This can be easily implemented for both the general 6R manipulator and polymers. Although the extended elimination method is computationally faster than the Jacobian method, in cases where some of the joint angles are 180° (i.e., where the elimination method fails), we combine these two methods effectively to obtain the full set of inverse kinematic solutions. We demonstrate our approach with several numerical examples.

This paper presents design, modelling and analysis of the selected Rigid ropes S-type Cable-suspended Parallel Robot (RSCPR). The characteristic of this system is its geometric construction which defines the kinematic model through the Jacobian matrix. The relationship between external and internal forces is defined by the Lagrange principle of virtual work. The Jacobian matrix is directly involved in the application of the Lagrange principle of virtual work and generation of the dynamic model of the RSCPR system. Selected examples of the CPR system types are analysed and the comparison of their results is presented. The software package named ORIGI has been developed for the RSCPR model verification.

Parallel mechanisms possess several advantages such as the possibilities for high acceleration and high accuracy positioning of the end effector. However, most of the proposed parallel manipulators suffer from a limited workspace. In this paper, a novel 6-DOF parallel manipulator with coaxial actuated arms is introduced. Since parallel mechanisms have more workspace limitations compared to that of serial mechanisms, determination of the workspace in parallel manipulators is of the utmost importance. For finding position, angular velocity, and acceleration, in this paper, inverse and forward kinematics of the mechanism are studied and after presenting the workspace limitations, workspace analysis of the hexarot manipulator is performed by using MATLAB software. Next, using the obtained cloud of points from simulation, the overall borders of the workspace are illustrated. Finally, it is shown that this manipulator has the important benefits of combining a large positional workspace in relation to its footprint with a sizable range of platform rotations.

A novel analytic approach is proposed for determining the singularities of some four degree of freedom (DOF) parallel manipulators (PMs). First, the constraint and displacement of a general 4-DOF PM are analyzed. Second, a common 3 × 4 translational Jacobian matrix Jν and a common 3 × 4 rotational Jacobian matrix Jω are derived, and a 4 × 4 general Jacobian matrix J of the 4-DOF PMs is derived from Jν and Jω. Since a complicated process to determine singularities from the 4 × 6 Jacobian matrix is transformed into a simple process to determine singularity from J, the singularities of the some 4-DOF PMs with 3 translations and 1 rotation, or with 3 rotations and 1 translation, or with combined translation–rotations are analyzed and determined easily by this approach.