Kazem Kazerounian

Global versus local optimization in redundancy resolution of robotic manipulators

In redundancy resolution of robotic manipulators with more than the required degrees of freedom at the kinematic level, the minimization of the Euclidean norm of the joint velocities at the dynamic level, and the minimization of the kinetic energy of the manipulator at any moment of the task execu tion have long been suggested in the literature. In this paper the global optimization of the above characteristics are worked out by using integral-type criteria. The results are in surprisingly simple and elegant forms and give new insights to the redundancy resolution of robotic manipulators. The relations between local and global optimization are discussed.

Efficient evaluation of spur gear tooth mesh load using pseudo-interference stiffness estimation method

This paper presents a new method, pseudo-interference stiffness estimation (PISE), for evaluating the equivalent mesh stiffness and the mesh load in gear system. The PISE method is based on evaluation of the geometric overlap of two assumedly rigid bodies and estimation of the contact force based on this artificial overlap area (or volume) and the singular stiffness (at the point of contact) of the bodies. Computationally, this procedure is orders of magnitude about 2000 times (in our numerical simulation) faster than finite element analysis of contacting bodies. This significant gain in computational efficiency leads itself to practical dynamic simulation of complex gear systems. In this paper, examples of two cylinders contact problem were solved by PISE method and finite element contact model. The results from both methods show reasonable agreement. PISE is then applied to gear teeth contact problem to estimate the equivalent mesh stiffness. The estimated results were compared with the finite element contact results. The comparison from PISE and finite element contact analysis also shows good agreement.

Improved numerical solutions of inverse kinematics of robots

Numerical solution of the inverse kinematics of robots using modified Newton-Raphson (MNR) and modified predictor-corrector (MPC) algorithms is discussed. These modified algorithms are highly reliable and stable. Both algorithms always find a solution if a physically realizable robot configuration exists. They are also capable of approaching singular configurations of the robot as E = C εm, where E is the error between the theoretical and numerically computed singular joint values,\epsivis the convergence criteria, and C and m are appropriate constants. It is also shown that the modified predictor-corector (MPC) algorithm is 5-15 times faster than the modified Newton-Raphson (MNR) algorithm.

Protofold: A Successive Kinetostatic Compliance Method for Protein Conformation Prediction

This paper presents an efficient and novel computational protein prediction methodology called kineto-static compliance method. Successive kineto-static fold compliance is a methodology for predicting a protein molecules motion under the effect of an interatomic force field without the need for molecular-dynamic simulation. Instead, the chain complies under the kineto-static effect of the force field in such a manner that each rotatable joint changes by an amount proportional to the effective torque on that joint. This process successively iterates until all of the joint torques have converged to a minimum. This configuration is equivalent to a stable, globally optimized potential energy state of the system or, in other words, the final conformation of the protein. This methodology is implemented in a computer software package named PROTOFOLD. In this paper, we have used PROTOFOLD to predict the final conformation of a small peptide chain segment, an alpha helix, and the Triponin protein chains from a denatured configuration. The results show that torques in each joint are minimized to values very close to zero, which demonstrates the methods effectiveness for protein conformation prediction.

From Mechanisms and Robotics to Protein Conformation and Drug Design

The systematic study of kinematics can be traced to the writings of the ancient Greeks, Egyptians, Romans and Persians as far back as 500 B. C. For many centuries kinematics (along with geometry) was regarded as one of the basic sciences that explained observed physical phenomena and was used to engineer machines. Though it may seem unlikely, kinematics (in particular, robot kinematics) can significantly contribute to our understanding of biological systems and their functions at the microscopic level and to the engineering of new diagnostic tools, treatments, and drugs for a variety of diseases. Given the vast body of knowledge in theoretical, applied, and analytical kinematics and robotics, the conspicuous absence of the kinematics community from current molecular science research relating to the prediction of protein folding, protein docking, protein engineering, and drug design seems puzzling. In this paper, we will discuss the potential contributions of kinematics to some current challenges in biotechnology.

A Real Parameter Continuation Method for Complete Solution of Forward Position Analysis of the General Stewart

Stewart Platform is a six degree of freedom, parallel manipulator, which consists of a base platform, a coupler platform and six limbs connected at six distinct points on the base platform and the coupler platform. The forward position analysis problem of Stewart Platform amounts to finding all its possible configurations based on the knowledge of the lengths of its limbs. In this paper, we present a numerical method for solving the forward position analysis problem for the most general Stewart Platform. This is a numerical method based on the polynomial continuation as established in recent works in the literature. However, one main difference is that the start system and the homotopy used here are based on physical design rather than pure mathematical equations. First, the target Stewart Platform is geometrically simplified into a platform, which, as the start platform, can be solved analytically. Then, a homotopy is constructed between the kinematics equations of the start platform and those of the target platform. By changing the parameters of the start platform incrementally into the parameters of the target system while tracking solutions of the start platform, a complete set of 40 solutions to the target platform can be found. Through this process, all of the extraneous paths have been eliminated before the solution tracking procedure starts and only isolated solutions of the start platform are tracked. The process for solutions to switch between real and complex is examined.

Analysis and Design of Protein Based Nanodevices: Challenges and Opportunities in Mechanical Design

Nanomachines are devices that are in the size range of billionths of meters 10−9 m and therefore are built necessarily from individual atoms. These devices will have intrinsic mobilities that result in their geometry change and hence enable them to perform specific functions. Futuristic scholars and researchers believe that nanodevices will one day be used as “assemblers” in the construction of new materials and objects from inside out 1 ; They will be able to “self replicate;” They will be able to enter biological cells to cure disease; They will be able to facilitate space travel; They will be used to clean up the environment; They will be the building blocks of the electronic circuitry and computers 2 . While these claims may prompt profound philosophical and scientific debates for many years to come, they offer humanity with the potential to eliminate poverty, pollution and disease. In the foreseeable future, nanodevices and molecular machines are expected to lead to breakthroughs in technology and life sciences. Impacted industries include Semiconductors molecular electronics, nanophotonics, memory , Microsystems micro electro-mechanical systems—MEMS, communications, optical, fluidics, rf , energy fuel cells, biomimetics, membranes, carbon systems , materials compounds, powders, polymers, nanostructures , biotechnology delivery, lab-on-chip, proteomics, genomics and medical drug design, molecular medicine .

Nano-Kinematics for Analysis Of Protein Molecules

Proteins are evolutions mechanisms of choice. The study of nano-mechanical systems must encompass an understanding of the geometry and conformation of protein molecules. Proteins are open or closed loop kinematic chains of miniature rigid bodies connected by revolute joints. The Kinematics community is in a unique position to extend the boundaries of knowledge in nano biomechanical systems. In this work, we have presented a comprehensive methodology for kinematics notation and direct kinematics for protein molecules. These methods utilize the zero-position analysis method and draws upon other recent advances in robot manipulation theories. The procedures involved in finding the coordinates of every atom in the protein chain as a function of the dihedral and Rotamer angles are computationally the most efficient formulation developed to date. The notation and the methodologies of this paper are incorporated in the computer software package PROTOFOLD and will be made available to individuals interested in using it. PROTOFOLD is a software package that implements novel and comprehensive methodologies for ab initio prediction of the final three-dimensional conformation of a protein, given only its linear structure. In addition to the new kinematics methodologies mentioned above, we have also included all the basic kinematic parameter values that are needed in any kinematic analysis involving proteins. While these values are based on a body of knowledge recorded in the protein data bank, they are presented in a form conducive to kinematics.

Mobility analysis of general bi-modal four bar linkages based on their transmission angle

Abstract The equation Z = (cos2μ) − 1 = 0, where μ is the transmission angle of an R-S-S-R four bar linkage, is shown to be a fourth order polynomial in t (the tangent of the half of the input angle). It is further shown that the mobility of the linkage is related to the number of the real roots of this quartic equation as follows: • 0 real roots: crank-rocker or drag link; • 2 real roots: double rocker; • 4 real roots: special double rocker or rocker (input)-crank. The conditions for the number of real roots are developed in terms of the explicit conditions on the linkage parameters. As subsets of these conditions, the Grashof mobility criteria for planar and spherical four-bars are developed.

Manipulator dynamics using the extended zero reference position description

A simplified description of robotic manipulator is in terms of its zero reference position. It requires the specification of the joint axes directions and the coordinates of points locating the joint axes in the base coordinate system. Manipulator dynamics is developed in an extended zero reference position description. The recursive Newton-Euler formulations for the problems of inverse and direct dynamics are presented.