A Recursive Algorithm for the Forward Kinematic Analysis of Robotic Systems Using Euler Angles

Forward kinematics is one of the main research fields in robotics, where the goal is to obtain the position of a robot’s end-effector from its joint parameters. This work presents a method for achieving this using a recursive algorithm that builds a 3D computational model from the configuration of a robotic system. The orientation of the robot’s links is determined from the joint angles using Euler Angles and rotation matrices. Kinematic links are modeled sequentially, the properties of each link are defined by its geometry, the geometry of its predecessor in the kinematic chain, and the configuration of the joint between them. This makes this method ideal for tackling serial kinematic chains. The proposed method is advantageous due to its theoretical increase in computational efficiency, ease of implementation, and simple interpretation of the geometric operations. This method is tested and validated by modeling a human-inspired robotic mobile manipulator (CHARMIE) in Python.

Multi-Criteria Design Optimization of Delta Robot with Four Degrees of Freedom

A delta robot with three degrees of freedom, having been well studied over the past 40 years, is one of the most popular parallel mechanisms. Nowadays, an urgent task is to study the properties of various modifications of this mechanism. The article considers a delta robot with four degrees of freedom, in which one of the kinematic chains with a parallelogram is divided into two, allowing the output link to have an additional rotational degree of freedom. To maximize the working area and minimize the cost of modification the optimization of the robot design was performed. The problem of maximizing a cubic workspace has been solved.

Sub-optimal Solution of the Inverse Kinematic Task of Redundant Robots without Using Lagrange Multipliers

In the paper a novel approach is suggested for solving the inverse kinematic task of redundant open kinematic chains. Traditional approaches as the Moore-Penrose generalized inverse-based solutions minimize the sum of squares of the timederivative of the joint coordinates under the constraint that contains the task itself. In the vicinity of kinematic singularities where these solutions are possible the hard constraint terms produce high time-derivatives that can be reduced by the use of a deformation proposed by Levenberg and Marquardt. The novel approach uses the basic scheme of the Receding Horizon Controllers in which the Lagrange multipliers are eliminated by direct application of the kinematic model over the horizon in the role of the ”control force”, and no reduced gradient has to be computed. This fact considerably decreases the complexity of the solution. If the cost function contains penalty for high joint coordinate time-derivatives the kinematic singularities are ab ovo better handled. Simulation examples made for a 7 degree of freedom robot arm demonstrate the operation of the novel approach. The computational need of the method is still considerable but it can be further decreased by the application of complementary tricks.

Inverse modeling of the stewart foot

The Stewart's leg is used today in the majority of parallel robotic systems, such as the Stewart platform, but also in many other types of mechanisms and kinematic chains, in order to operate them or to transmit motion. A special character in the study of robots is the study of inverse kinematics, with the help of which the map of the motor kinematic parameters necessary to obtain the trajectories imposed on the effector can be made. For this reason, in the proposed mechanism, we will present reverse kinematic modeling in this paper. The kinematic output parameters, ie the parameters of the foot and practically of the end effector, ie those of the point marked with T, will be determined for initiating the working algorithm with the help of logical functions, "If log(ical)", with the observation that here they play the role of input parameters; it is positioned as already specified in the inverse kinematics when the output is considered as input and the input as output. The logical functions used, as well as the entire calculation program used, were written in Math Cad.

Improving Machining Accuracy for a Robotic Arm with Hybrid Kinematic Chains Based on Deformation Characteristics

The joint deformation has great influence on machining accuracy for a robotic arm. In this paper, the deformation characteristics of the robotic arm with hybrid kinematic chains is investigated in order to improve its machining accuracy. Firstly, the deformation model of the joints has been established based on the Strain energy method and Castigliano theorem according to the robot structure. Secondly, the deformation influence coefficient (DIC) is defined to investigate the deformation influence of main components on the end-effector, and the deformation characteristics are evaluated by the simulation. Finally, a small size robotic arm prototype is established and robotic drilling comparative experiments are conducted. The theoretical and experiment results show that the machining method can be selected according to the DIC, which the force can be applied to the components with better stiffness. On the other hand, the deformation of driving components can also be reduced when the DIC cannot be adjusted to meet the accuracy requirement.

A geometrical formulation for the workspace of parallel manipulators

In study this paper, a geometric formulation is proposed to describe the workspace of parallel manipulators by using a recursive approach as an extension of volume generation for solids of revolution. In this approach, the workspace volume and boundary for each limb of the parallel manipulator is obtained with an algebraic formulation derived from the kinematic chain of the limb and the motion constraints on its joints. Then, the overall workspace of the mechanism can be determined as the intersection of the limb workspaces. The workspace of different kinematic chains is discussed and classified according to its external shape. An algebraic formulation for the inclusion of obstacles in the computation is also proposed. Both analytical models and numerical simulations are reported with their advantages and limitations. An example on a 3-SPR parallel mechanism illustrates the feasibility of the formulation and its efficiency.

GENERIC MODEL FOR GONIOPHOTOMETER GEOMETRIES

In this work, we present a method to describe the model of a goniophotometer for uncertainty analysis by state-of-the-art Universal Robotic Description Format (URDF). The parameters of the kinematic chain model are determined by measurements of the geometric properties of the goniophotometer. The uncertainties of the pose are determined using Monte Carlo (MC) simulations of the kinematic chain. The measured geometric uncertainties are input the MC simulations. The proposed framework enables high level description of kinematic chains for MC simulations of measurement systems. Furthermore, the uncertainty of the total system is demonstrated over the MC trials to prove a sufficient amount of MC trials. The results of this generic approach are evaluated against an existing model and the uncertainty determination of the same goniophotometer.

MEANS, STANDS AND MACHINES FOR TESTING GEAR WHEELS AND GEAR TRAINS OF HELICOPTER REDUCTION TRAINS

The production and repair of such high-tech and important products as helicopters‟ reduction trains is impossible without comprehensive testing of these products, starting with the manufacture of their individual parts and assemblies and ending with the delivery of reduction trains to the customer. Various means for testing of gear wheels‟ rims and gear trains of helicopter‟s reduction trains, which have found application in testing equipment, are presented. Devices, testers, stands and machines for various tests are considered in order to control the characteristics of gear trains of aviation reduction trains after certain periods of their operation and repair, aimed at achieving better performance during further operation. The considered traditional metrological means of control of gear rims, gear measuring machines and complexes, some stands and machines for testing of reduction trains, pulse controllers and roll machines give an idea of various methods and means of control of gear wheels and gear trains of helicopters‟ reduction trains. The main method of experimental research of gear trains of reducers is stand tests both on movable gear wheels and on roll machines. Until recently, the most common method for monitoring and diagnosing gear trains has been vibrography, however, existing techniques do not give an accurate picture of the train condition, especially the contact surface of the teeth. During the operation of the gear train as a part of the helicopter‟s reduction train, signals from other sources (rotors, blades, shafts, bearings) are superimposed on the vibration signal generated by the gear train which significantly complicates the extraction and processing of the desired vibration signal. One of the most effective methods for monitoring and diagnosing the technical condition of kinematic chains of different complexity, which includes gear trains of helicopters„ reducers is kinematometry. The disadvantage of traditional kinematometry is the need to use high-precision sensors for the frequency and phase of the rotor rotation. Control of vibration from the early 1990s to the present time is the most advanced control, the means and methods of which are well developed in the aviation industry.