Instantaneous Center Research Articles

A general method for the determination of the instantaneous screw axes of one-degree-of-freedom spatial mechanisms

Abstract. This contribution shows that a method proposed previously, for the determination of the instantaneous centers of rotation of planar closed chains, can be generalized for the determination of the instantaneous screw axes of general one-degree-of-freedom spatial mechanisms. Hence, the approach presented in this paper can be applied to any of the closed chains that belong to any of the subgroups of the Euclidean group, SE(3), namely planar, spherical or chains associated with the Schönflies subgroups, among others. Furthermore it can be also applied to multi-loop mechanisms and even to closed chains that are exceptional o paradoxical, as indicated by Hervé.

Software-Engineering Optimization with Mathematical Method Improvements for Numerical Reuleaux Method

This paper presents an extension both in software optimization with simulations and detailed mathematical theory of Numerical Reuleaux Method based on previous publications. In the literature, there are a number of papers in Numerical Reuleaux Method and its applications (Aerospace, Helicopter Dynamics in Turbulence Conditions, Biomedical Engineering, Biomechanics, etc) since 2007. This contribution is a detailed presentation of the mathematical framework that constituted the basis for those articles along 2007-2020. The Classical Reuleaux Method (<strong>CRM</strong>) is frequently used in Physical Dynamics, Engineering Mechanics and Bioengineering to determine the Instantaneous Rotation Center (<strong>IRC</strong>) of a rigid body in arbitrary movement. The generic mathematical <strong>CRM </strong>only can be applied on rigid bodies, whose shape remains constant during the movement. If the solid in movement is a Pseudo-Rigid Body (<strong>PRB</strong>), the <strong>CRM </strong>has to be modified numerically to conform the shape changes and adapt on the density distribution variations of the <strong>PRB </strong>(we denominate it, in this case<sup>1</sup>, <strong>The Numerical Reuleaux Method</strong>, <strong>NRM</strong>). This Geometrical-Numerical Approximation Method is based on the division of the Pseudo-rigid body into small volume parts called voxels (roughly speaking parallelepipedic), namely, voxelization of the body subject to dynamics. The theoretical basis of the method is strictly shown in complementary details, with the necessary Theorems and Propositions of the model. Nonlinear Optimization Techniques that support the initial theory have been developed, and the Error boundaries with Error reduction techniques are determined. Computational Simulations have been carried out to prove the <strong>NRM </strong>Theoretical Model feasibility and numerical veracity of the Propositions, Theorems, and Error Boundaries. Appropriate software was made to carry out these simulations conveniently. The initial results agree to the theoretical calculations, and the IRC computation for 2 voxels shows to be simple and easy. Some initial guidelines for a theoretical development of this algorithm applied on large pseudo-rigid bodies, by using Monte-Carlo techniques, are sketched. Recent applications, Aerospace and Biomechanics, are also shown.

Paths of the cervical instantaneous axis of rotation during active movements-patterns and reliability.

The instantaneous helical axis (IHA) is a characteristic of neck movement that is very sensitive to changes in coordination and that has potential in the assessment of functional alterations. For its application in the clinical setting, normative patterns must be available, and its reliability must be established. The purpose of this work is to describe the continuous paths of the IHA during cyclic movements of flexion-extension (FE), lateral bending (LB), and axial rotation (AR) and to quantify their reliability. Fifteen healthy volunteers participated in the study; two repetitions were made on the same day (by different operators) and over an 8-day interval (by the same operator) to evaluate the inter-operator and inter-session reliability, respectively. The paths described by the IHA suggest a sequential movement of the vertebrae in the FE movement, with a large vertical displacement (mean, 10cm). The IHA displacement in LB and AR movements are smaller. The paths described by the IHAs have a very high reliability for FE movement, although it is somewhat lower for LB and RA movements. The standard error of measurement (SEM) is less than 0.5cm. These results show that the paths of the IHA are reliable enough to evaluate changes in the coordination of intervertebral movement. Graphical abstract A video photogrammetry system is used to record the cyclic movements of the neck, from which the continuous trajectories of the associated instantaneous helical axis (IHA) are calculated. We have analyzed the movements of flexion-extension (FE), lateral flexion (LB), and axial rotation (AR) for a sample of 15 healthy subjects. The measurements have been repeated with two different operators (in the same session) and in two separate sessions (same operator). IHA displacement patterns have been obtained in each movement, and the reliability of the measurement of such IHA trajectories has been estimated.

Ankle Control in Walking and Running: Speed- and Gait-Related Changes in Dynamic Mean Ankle Moment Arm.

The human foot-ankle complex uses heel-to-toe ground contact progression in walking, but primarily forefoot contact in high-speed running. This qualitative change in ankle control is clear to the runner, but current measures of ankle behavior cannot isolate the effect, and it is unknown how it changes across moderate speeds. We investigated this dynamic ankle control across a range of walking and running speeds using a new measure, the dynamic mean ankle moment arm (DMAMA): the ratio of sagittal ankle moment impulse to ground reaction force impulse on a single limb. We hypothesized that DMAMA would increase with speed in both walking and running, indicating more forefoot-dominated gait with ground reaction forces more anterior to the ankle. Human subjects walked (1.0-2.0 m/s) and ran (2.25-5.25 m/s) on an instrumented treadmill with motion capture and pressure insoles to estimate DMAMA. DMAMA decreased with increasing walking speed, then increased upon the transition to running, and increased further with increasing running speed. These results provide quantitative evidence that walking becomes more hindfoot-dominated as speed increases-similar to behavior during acceleration-and that running is more forefoot-dominated than walking. The instantaneous center of pressure (COP) at initial ground contact did not follow the same trends. The discrepancy highlights the value of DMAMA in summarizing ankle control across the whole stance phase. DMAMA may provide a useful outcome metric for evaluating biomimetic prostheses and for quantifying foot contact styles in running.

Nonlinear analysis of pile groups subjected to combined lateral and torsional loading

An empirical approach has been developed to analyze the nonlinear response of a pile group with arbitrarily distributed piles subjected to combined lateral and torsional loading. In this approach, the concept of instantaneous twist center is applied to analyze the displacement relationship of pile heads and establish the static equilibrium equations of the pile cap. The horizontal interaction among the individual piles is considered through the generalized p-multiplier. The coupling effect of lateral resistance on the torsional resistance of each pile is quantified using an empirical factor β; the lateral and torsional nonlinear responses of individual piles are modeled by p-y and τ-θ curves, respectively. The proposed approach not only captures the most significant aspect of the group effect and coupling effect in a pile group subjected to combined lateral and torsional loading, but also automatically updates p-multipliers of individual piles based on pile cap displacements. The proposed approach was verified using results of model tests on pile groups subjected to lateral loading, torsional loading, and combined lateral and torsional loading, separately. In general, the pile cap response and the transfer of applied loads in the pile groups agree well with the test results.

CONCEPTUAL DESIGN OF AUTONOMOUS CART FOLLOWER FOR WHEELCHAIR USER

This paper focuses on kinematics of the cart follower and the system identification of propulsion system by using brushed DC motor. The cart follower uses Ackermann configuration as the steering system. The modeling of kinematics equation takes into account the instantaneous center of rotation (ICR), velocity of each tire, heading angle, and simple movement of the cart. The cart is propelled by transaxle brushed DC motor. It is important to approximate an accurate transfer function to represent the motor as the plant module is unavailable. The motor is simulated by using Arduino hardware package in MATLAB®. Rotary encoder is used to record the angular velocity of the shaft. MATLAB® code is created in order to calculate the linear velocity and tabulate the datasets. System Identification Toolbox determines the transfer function of the motor and its performance. The variables measured in experiment to identify the transfer function of the DC motor system are output angular velocity and input voltage. The parameters taken from the DC motor’s mathematical model are derived based on existing literatures. The graph of output velocity against time is plotted and the transfer function is estimated by using System Identification Toolbox in MATLAB®. From the results, it is demonstrated that the motor exhibits second order system.
 Keywords: Cart follower, wheel mobile robot, kinematics, system identification

Optimal Design of a Novel 3-DOF Orientational Parallel Mechanism for Pelvic Assistance on a Wheelchair: An Approach Based on Kinematic Geometry and Screw Theory

Pelvis mobility is essential to the daily seated activities of wheelchair users, however it is not yet fully addressed in the field of active wearable devices. This letter presents a novel design and optimization methodology of an in-parallel actuated robotic brace for assisting the human pelvis during seated maneuvers on wheelchair. This design uses human data captured by cameras in conjunction with the knowledge of kinematic geometry and screw theory. The mechanism has full rotational three degrees-of-freedom (DOFs) and also accommodates coupled translation of the human pelvic segment. This type of motion was realized by employing three kinematic limbs that impose non-intersecting zero-pitch constraint wrenches on the platform. Our multi-objective optimization (MOO) routine consists of two stages: (I) platform constraint synthesis, where the geometric parameters of the limb constraints were determined to minimize the pelvis-platform errors of trajectories and instantaneous screw axes (ISAs); and (II) limb structural synthesis, where limb types and dimensions, workspace, transmission performances, singularities, and actuated joint displacements were considered. The optimized mechanism has an asymmetrical [RRR]U-2[RR]S architecture. This mechanism can also be integrated into our previously developed Wheelchair Robot for Active Postural Support (WRAPS).

A SPECIAL CASE OF CONGRUENT CENTROIDS OF NONCIRCULAR WHEELS FORMED BY ARCS OF THE LOGARITHMIC SPIRAL

Rolls of congruent curves one by one without sliding, which are arcs of logarithmic spiral, are considered. Two symmetrical arcs form a closed loop with a common pole of the polar coordinate system. This figure resembles a known heart symbol with a pole on the line of symmetry. The article shows and mathematically proved that with the proper choice of the distance between the poles of such figures, they can be rolled one by one, rotating around their poles. If one figure is rolled over the other, the geometric location of the instantaneous centers of rotation with respect to the fixed figure lies on the contour of this figure and represents a space centroid, and in the moving figure system forms a moving centroid. The moving centroid rolls without sliding over the stationary. If fixed and moving centroids have points whose distance from the contact point is constant, then the point of the moving centroid will describe the circle which center is at the point of the fixed centroid. If these points are taken as centers of rotation of both centroids, then the rolling of the moving centroid by the fixed one can be replaced by the rotational motion of both centroids around the stationary centers. The point of contact of the centroids during their rotation is in a segment that connects the centers of rotation and makes some movement on it. If the centroids are circles, then the point of contact is fixed on the line joining their centers. Of particular interest are congruent centroids, such as circles of the same radius. In this case, the manufacture of both centroids is the same. If you shift the center of rotation of the circle at definite value, than the second centroid will be the so-called noncircular wheel, which can be built by a well-known algorithm. However, finding congruent noncircular wheels presents some difficulties. A known case of such wheels are centroids in the form of congruent ellipses whose centers of rotation are located in one of the focuses. By reducing the eccentricity of both ellipses, they approach the circle and turn into it at zero value of this indicator. The paper shows that a similar transformation is possible for congruent centroids formed from arcs of the logarithmic spiral. An analytical description of the centroids was made and their images were created with a common point of contact for different angles of rotation.

A solution-region approach for synthesis linkages with coincident instantaneous center and one fixed pivot

We present a solution-region based approach for the synthesis of straight-line linkages, which is based on the stationary curvature point on curve and higher order stationery point theory of infinite approximation geometry. The selection of the Ball-Burmester point and the distribution of the solution-regions are discussed in this work. Further, two alternative cases have been analyzed for finding the Ball-Burmester point positions of the crank-rocker straight-line mechanism, when one side-link is collinear with the frame. The distribution diagrams of the Ball-Burmester point positions are depicted to help the designers extract complete solutions. Infinite solutions for the mechanism can be expressed for each case on a diagram by employing the solution-region method. These diagrams will help the designers find the inherent mechanism intuitively and streamline the selection of results. The results indicate that the efficiency of design and reliability have been effectively improved owing to the implementation of these methods.

Total disc arthroplasties change the kinematics of functional spinal units during lateral bending

BackgroundInformation about kinematics in different functional spinal units before and after total disc arthroplasties is necessary to improve prostheses and determine indications. There is little information about the nonstationary instantaneous helical axis of rotation under lateral bending in the cervical spine before and after total disc arthroplasty. MethodsKinematic analyses were performed with an established measuring apparatus on 8 human functional spinal units (C3/C4, C5/C6) under intact conditions and after total disc arthroplasty with two different types of prostheses: Bryan and Prestige. The instantaneous helical axis, migration, and stiffness of the segments were calculated. FindingsThe instantaneous helical axis direction was always inclined ventrally. Ventral inclination was significantly higher in segment C3/C4 than in segment C5/C6 under all conditions (p < 0.001). Both types of arthroplasties significantly increased ventral inclination compared to intact conditions. In both segments, the path length of the instantaneous helical axis' migration was significantly longer after total disc arthroplasty with Bryan (p = 0.001) and shorter after Prestige (p < 0.001) prostheses than under intact conditions. After both types of arthroplasties, the migration path length was significantly longer and the stiffness was significantly lower in segment C3/C4 than in segment C5/C6. InterpretationBoth types of arthroplasties changed the kinematics of both segments during lateral bending. Altered instantaneous helical axis migration, greater ventral inclination and less stiffness after both arthroplasties indicate unphysiological motion. Both arthroplasties had greater impact on segment C3/C4 than on segment C5/C6 in terms of hypermobility. Increased translational motion after total disc arthroplasty with a Bryan prosthesis might be caused by the prosthetic design.

A novel methodology for determining the singularities of planar linkages based on Assur groups

In this paper, a simple and effective methodology for judging the singularities of planar linkages is presented, which is based on Assur groups. The methodology determines the geometrical configurations of the Assur groups in singularities. Based on the singularities of a simple two-bar group, the possible singularities of all Assur four-bar and six-bar groups are given by the concept of instant centers. Then the general process and rules of determining singularities are obtained and shown through several examples of the 1-DOF planar linkages. These linkages include the two six-bar linkages and the several eight-bar linkages composed of Assur six-bar groups. The singularities of them verify the proposed methodology, which reveals that the singularities of a linkage only depend on the Assur groups. Therefore, as long as the singularities of Assur groups are determined, all the possible singularities of the linkage composed of these groups can be determined. This methodology is independent of linkages, so it is universal for all planar multi-bar linkages which can be divided into these Assur groups.

Total disc arthroplasties alter the characteristics of the instantaneous helical axis of the cervical functional spinal units C3/C4 and C5/C6 during flexion and extension in in vitro conditions

Total disc arthroplasty (TDA) increases the risk of adjacent segment disease (ASD). Kinematic analyses are necessary to compare the intact condition (IC) with alterations after TDA to develop better prostheses. A well-established 6D measuring apparatus (resolution < 2.4 μm; 400 positions/cycle) was used. Kinematics of the flexion and extension of 8 human cervical spine segments (cFSU) C3/C4 and C5/C6 (67.9 ± 13.2 y) were analyzed in the IC and after TDA (Bryan® Cervical Disc [B-TDA], Prestige LP® Cervical Disc [P-TDA]). The migration of the instantaneous helical axis (IHA) and the stiffness of the segments were calculated. Analyses demonstrated a stretched U-curved IHA migration in the sagittal plane. The IHA positions were significantly more cranial in cFSU C5/C6 than in C3/C4 in IC and after either TDA (IC: p < 0.001; B-TDA: p = 0.001; P-TDA: p = 0.045). In cFSU C3/C4 IHA positions shifted anteriocranially after either TDA (p < 0.001). In cFSU C5/C6, the IHA positions were significantly more anterocranial after B-TDA than in IC and after P-TDA (anterior: p < 0.001; cranial: p = 0.005). After B-TDA, the IHA migration path length was significantly longer in cFSU C3/C4 than in C5/C6 (p = 0.007) and longer than in IC in both cFSU (C3/C4: p = 0.047; C5/C6: p < 0.001). Stiffness was increased after both TDA. Various kinematic alterations were observed after both TDA. Increased translation and IHA position shifting after both TDA might indicate abnormal strain and a derogated benefit of TDA. These results imply the most abnormal strain after B-TDA. The lower cFSU might be more susceptible to alterations after TDA than the upper cFSU.

Investigation of lumbar spine biomechanics using global convergence optimization and constant loading path methods.

Computational models and inverse dynamic optimization methods are used to predict in-vivo spinal loading. Spinal force is conventionally predicted using the constant loading path method, which is based on the concept that the physiological directions of the spine loads follow the same path of the spinal curve. However, the global convergence optimization method, in which the instantaneous center of rotation of the joint should be also predicted, is necessary for accurate prediction of joint forces of the human body. In this study, we investigate the joint forces, instantaneous centers of rotation, and muscle forces of the human lumbar spine using both global convergence optimization method and constant loading path method during flexion, upright standing, and extension postures. The joint forces predicted using the constant loading path method were 130%, 234%, and 253% greater than those predicted using the global convergence optimization method for the three postures. The instantaneous centers of rotation predicted using the global convergence optimization method were segment level-dependent and moved anteriorly in the flexion and posteriorly in the extension, whereas those predicted using the constant loading path method moved posteriorly in both the flexion and extension. The data indicated that compared to the global convergence optimization method, the constant loading path method introduces additional constraints to the spinal joint model, and thus, it results in greater joint and muscle forces.

Research on the transmission error of swing-rod movable teeth transmission system

Using the two-tooth difference swing-rod movable teeth transmission system satisfying the drive function of large optical instruments as the study object, the influence of each component error on system transmission error is analysed. Each component error is presented by the vector method, and then it is transformed into equivalent error in the direction of the meshing action line based on the equivalent meshing error principle. The instantaneous transmission ratio of the system is obtained by the instantaneous velocity center method, and the system transmission error model is established. Using numerical analysis, the influence of each component error on the system transmission error is obtained. The transmission error test platform is used to test and analyze the transmission error of the two-tooth difference swing-rod movable teeth transmission system. The research results show that the swing-rod length error and the wave generator eccentric error have a great influence on the transmission error of the system among the six types of error factors, so they should be strictly controlled during design, processing and assembly. This study provides a theoretical basis for the rational allocation of machining errors and assembling errors of the two-tooth difference swing-rod movable teeth transmission system.

Influence of hinged device parameters on negative resonance oscillations during the operation of machine-tractor unit in transport mode

Annotation Purpose. Reducing the influence of resonance phenomena on the structural elements of a tractor of the KIY 14102 type when driving with an attached implement in transport mode. Methods. To solve this problem means of graph-analytical constructions, analytical geometry, oscillation theory and theoretical mechanics were used. Results. On the basis of the graphic-analytical analysis of the kinematic diagram of the tractor attachment of the KIY 14102 type, it was found that the position of the instantaneous center of its rotation significantly depends on the change in the angle between the tractor frame and the levers, which are united by the CA-1 automatic connection device. The frequency range of forced oscillations of the tractor frame, which occur when driving in a certain speed range, can coincide with the relative natural frequency of the tractors, which leads to resonance phenomena. Resonant longitudinal-angular vibrations of the tractor frame reduce the normal reactions of the steered wheels with the supporting surface, which worsens controllability. Changing the frequency of the natural resonance of the elements connecting the tractor with the implement can be done by changing the kinematic stiffness of the mounted system. Conclusions 1. The kinematic diagram of the hinged device of tractors significantly affects the dependence of the position of the instantaneous center of rotation of the hinged device relative to the mass of the implement that is aggregated. 2. The existing parameters of the mounted systems of tractors of the KIY 14102 type can lead to the occurrence of resonance phenomena when driving in transport mode on unpaved field roads, which negatively affects the controllability of the MTA. 3. Reducing the resonant frequency of natural vibrations of the attachment system with the tool, by reducing the kinematic stiffness, improves the dynamics of the interaction of the elements of the machine-tractor unit with each other and with the supporting surface. Keywords: machine-tractor unit, clutch system, tests, dynamic loads, strain gauge measurements, air pressure in tires.

The effect of anisotropy on the interaction of the caterpillar propeller with the soil during the vehicle turn

The article discusses the force interaction of the caterpillar propeller with the ground during the vehicle turn. Since more than 70 % of soil reactions are inherently friction forces, the article is based on the Fyodor Opeiko mathematical theory of friction. According it, the resulting force and the moment of friction are interrelated quantities determined by the position of the instantaneous center of sliding. With increasing the moment of friction, the force decreases and vice versa. Since any caterpillar mover has lugs, its interaction with the soil in the longitudinal and transverse directions becomes different. In the frame-work of the adopted approach, the anisotropy of the force interaction of the propulsion with the soil is ex-pressed in various friction coefficients in the longitudinal and transverse directions. In addition, there is a fundamentally different nature of the interaction with the soil. In the transverse direction, a clean cut is observed. In the longitudinal direction, before the start of the cut, the soil is crushed due to its elastic properties. The article presents a mathematical model of the force interaction of a caterpillar propeller with soil, taking into account the anisotropy of the interaction. The elastic properties of the soil in the longitudinal direction are taken into account due to the variable coefficient of friction introduced under the integral sign. Hyperbolic tangent is used as a function, since it allows one to introduce the smallest number of empirical coefficients. Based on the presented mathematical model of force interaction, numerical calculations were performed. The results are presented in graphical form, which allows to visually as-sess the effect of anisotropy. The calculations showed that the differences in the values of the friction force due to taking into account anisotropy can reach 50 %, and the moment of friction up to 10 %.

Estimating the Instantaneous Screw Axis and the Screw Axis Invariant Descriptor of Motion by Means of Inertial Sensors: An Experimental Study with a Mechanical Hinge Joint and Comparison to the Optoelectronic System.

The motion of a rigid body can be represented by the instantaneous screw axis (ISA, also known as the helical axis). Recently, an invariant representation of motion based on the ISA, namely, the screw axis invariant descriptor (SAID), was proposed in the literature. The SAID consists of six scalar features that are independent from the coordinate system chosen to represent the motion. This method proved its usefulness in robotics; however, a high sensitivity to noise was observed. This paper aims to explore the performance of inertial sensors for the estimation of the ISA and the SAID for a simple experimental setup based on a hinge joint. The free swing motion of the mechanical hinge was concurrently recorded by a marker-based optoelectronic system (OS) and two magnetic inertial measurement units (MIMUs). The ISA estimated by the MIMU was more precise, while the OS was more accurate. The mean angular error was ≈2.2° for the OS and was ≈4.4° for the MIMU, while the mean standard deviation was ≈2.3° for the OS and was ≈0.2° for the MIMU. The SAID features based on angular velocity were better estimated by the MIMU, while the features based on translational velocity were better estimated by the OS. Therefore, a combination of both measurements systems is recommended to accurately estimate the complete SAID.

Most often instantaneous rotation center (MOIRC) for roll damping assessment in the free decay test of a FPSO

The previous study of Fernandes et al. [1] showed that rather than a fixed rotation center, the phenomenology can be better represented by the concept of a MOIRC. This study contributes to understanding Instantaneous Rotation Centers (IRC) and Most Often Instantaneous Rotation Centers (MOIRC) behavior during the free roll decay tests of a FPSO by following the time series of the IRC. It is important from a practical standpoint to understand that IRC behavior leads to distinct damping values. The work shows that the time series trace of the vertical position of the IRC resembles a tangent-form for lower damping. But when the damping increases, the time series trace changes to double parabolic type (one parabola with concavity downwards and another with concavity upwards). Consequently, the MOIRC changes its positions. The effect of the MOIRC on roll damping as a consequence of vortex generation on bilge keels has for half cycles. It explains why the damping is different from the clockwise to the counterclockwise oscillation, finally a point of finding out that considering the IRC is important for roll damping assessment. The linear and nonlinear analyses, also presented, have qualitatively confirmed the observations from the experimental analysis.

Development of a Passive Modular Knee Mechanism for a Lower Limb Exoskeleton Robot and Its Effectiveness in the Workplace

Quasi-passive or passive mechanisms used for exoskeleton robots for load-carrying augmentation have been developed for reducing development cost, robot weight, and external energy consumption for augmentation. These mechanisms have been developed based on biomechanical analyses of specific motions; however, few mechanisms do not include mechanical elements, such as springs and dampers. In this paper, a movable instantaneous center of rotation (M-ICR) linkage mechanism developed for the knee in the lower extremity exoskeleton without using mechanical elements is presented. Wearability and augmentation functions are considered. Based on these functions, design optimization is achieved using the PIAnO tool. To verify the augmentation function, the Solidworks tool is used. To verify the effectiveness of the M-ICR knee mechanism, oxygen consumption and the vertical ground reaction force are measured while walking with a barbell (0 kg, 10 kg, 20 kg) and while standing with a grinder with and without wearing the exoskeleton robot.

Design and kinematics of a 3-D printed walking robot “Big Foot”, overcoming obstacles

The proposed study presents an original concept for the design of a walking robot with a minimum number of motors. The robot has a simple design and control system, successfully moves by walking, avoids or overcomes obstacles using only two independently controlled motors. Described are basic geometric and kinematic dependencies related to its movement. It is proposed optimization of basic dimensions of the robot in order to reduce energy losses when moving on flat terrain. Developed and produced is a 3-D printed prototype of the robot. Simulation and experiments for overcoming an obstacle are presented. Trajectories and instantaneous velocities centers of links from the robot are experimentally determined. The phases of walking and the stages of overcoming an obstacle are described. The theoretical and experimental results are compared. The suggested dimensional optimization approaches to reduce energy loss and experimental determination of the instant center of rotation are also applicable to other walking robots.