Leg Mechanism Research Articles

Reconfiguration and compensation design method for single-DoF closed-chain leg mechanism

Compared with a wheeled robot propelled by a rotary drive, a legged robot equipped with multiple motors on a single leg possesses superior adaptability, while at the cost of high energy consumption and less velocity. Inspired by the California mite, the design method of reconfigurable closed-chain leg mechanism with single degree of freedom (DoF) is proposed for effective striding and smooth propelling. Furthermore, the lower-mobility closed-chain leg mechanism is more appropriate for obtaining high frequency and fast movement with the merits of simple control system and rotary drive. Firstly, a reconfigurable design is performed in the swing phase for a high-knee motion intermittently driven by a walking motor through dynamic coupling. Secondly, its fluctuations in vertical displacement and horizontal speed are compensated through the contact outline curve and variable speed input in the supporting phase. Finally, the simulated performance is analyzed and compared, and a prototype is fabricated for fluctuating and obstacle-crossing experiments.

Design and Analysis of a Planar Six-Bar Crank-Driven Leg Mechanism for Walking Robots

This study presents the design and a thorough analysis of a six-bar crank-driven leg mechanism integrated with a skew pantograph, developed for walking robots. The mechanism’s dimensions were optimized using a rigorous dimensional synthesis process in GIM software (version 2024). Subsequently, a detailed kinematic analysis was performed in GIM to simulate the leg’s motion trajectory, velocity, and acceleration. In parallel, kinematic equations were formulated using the vector loop method, implemented in MATLAB (version R2013-b), and compared with the GIM results for validation, demonstrating the strong agreement between both tools. These results confirm the mechanism’s ability to generate a compact, high-lift foot trajectory while maintaining system stability and energy efficiency. An inverse dynamic analysis was carried out to determine the actuator’s driving torque, ensuring efficient operation under expected load conditions. Furthermore, topology optimization conducted in SOLIDWORKS (version 2021) significantly reduced the weight of the ground-contacting link while preserving its structural integrity. A subsequent stress analysis validated the mechanical viability of the optimized design, supporting its feasibility for real-world implementation. This research provides a robust foundation for the development of a functional prototype. Its potential applications include mobile robots for sectors such as agriculture and all-terrain vehicles, where efficient, reliable, and adaptive locomotion is crucial. The proposed mechanism strikes an optimal balance between mechanical simplicity, cost-effectiveness, and high performance, making it well-suited for challenging operational environments.

Design and Experiment of an Independent Leg-Type Chassis Vehicle Attitude Adjustment System

In response to the current low work efficiency of soil ridge-working machinery, as well as its poor stability, passability, and adaptability, this paper designs an independent leg-type working platform that can autonomously adjust its vehicle attitude through LiDAR scanning in a soil ridge-working environment. The platform, in terms of its mechanism and structural design, adopts dual parallelogram mechanisms, dual lead screw mechanisms, and independent column leg mechanisms, with a maximum adjustable ground clearance of 107 mm and a maximum wheelbase adjustment of 150 mm. A gyroscope is mounted at the center of the platform for attitude adjustment, ensuring the accurate data collection of the ultrasonic ranging module. Moreover, the platform adopts an adaptive adjustment method based on vehicle attitude and soil ridge shape parameters, obtaining soil ridge parameters through LiDAR and combining ultrasonic ranging module data with stepper motor pulse signals to obtain the absolute vehicle attitude parameters, using first and second linear regression methods to adjust the vehicle attitude and other working parameters. A prototype was also created, and the test data from the soil obtained through experiments show that, after leveling with the gyroscope leveling algorithm, the average value of the pitch angle is up to 0.6154°, and the average value of the roll angle is up to 0.9989°, with the maximum variance of the pitch angle being 0.0474° and the maximum variance of the tilt angle being 0.1320°. After the ultrasonic ranging module data are filtered by the Kalman filter, the maximum variance is 0.0304, and after applying the final fusion algorithm, the maximum variance is only 0.0085. The LiDAR measurement width value deviates from the actual width value by no more than 1.0 cm, and the LiDAR measurement height value deviates from the actual height value by no more than 1.0 cm. The platform’s actual adjusted width deviates from the actual soil ridge width by no more than 2.0 cm, and the platform’s actual adjusted height deviates from the actual soil ridge height by no more than 1.2 cm. This platform can improve the passability, adaptability, and stability of agricultural machinery in soil ridge work and provide technical references for subsequent related research.

Kinematic synthesis and mechanism design of a six-bar jumping leg for elastic energy storage and release based on dead points

Small jumping robots widely adopt complex catapult mechanisms. This paper presents a novel jumping strategy using dead point instead of traditional catapult mechanisms, achieving efficient energy storage and release without increasing mechanical complexity. Single degree-of-freedom (DOF) planar six-bar linkages are widely used in bionic mechanism design due to their simple control and strong design flexibility. However, their complex configuration and numerous parameters make it challenging to carry out multi-objective and multi-constraint designs. In this paper, a design method of single DOF six-bar linkages based on dead-point constraints is proposed to design a frog-inspired leg mechanism. By enumerating the basic configuration atlas and using a stepwise closed-loop method, initial value screening is completed to improve the efficiency of objective function optimization. The dead-point constraints are simplified with graphical geometric properties. The resulting mechanism satisfies multiple objectives and constraints, including shape, motion posture and trajectory, demonstrating the feasibility of the method. Simulations and experiments confirmed the excellent jumping performance of the 147.1-g prototype, with a jump height of 8.55 times leg length and an energy-storing capacity of 35.39 J/kg.

The functions of leg muscles, structures and mechanisms in running.

The actions of the major human leg muscles are well established; however, the functions of these muscle actions during steady running remain unclear. Here, leg structures and mechanisms are considered in terms of their functions in meeting the task of a vehicle acting as an effective machine, supporting body weight during translation with low mechanical work demand and in supplying mechanical work economically. Legs are modelled as a sequence of linkages that predict muscle actions and reveal the varying muscle functions within the integrated leg. Work avoidance is achieved with isometric muscles and linkages that promote a sliding of the hip over the ground contact, resulting in an approximately horizontal path of the centre of mass. Economical work supply requires, for muscle with constrained power, shortening over the entire stance duration; this function is achieved by the hamstrings without disrupting the linkages resulting in work avoidance. In late stance, the two functions occur through coactivation of antagonistic muscles, providing one answer to Lombard's paradox. Quadriceps and hamstring tensions result in opposing moments about both hip and knee joints, but by doing so perform the independent yet complementary roles of work avoidance during translating weight support and economical work supply.

Picotaur: A 15 mg Hexapedal Robot with Electrostatically Driven, 3D‐Printed Legs

Dynamic and agile locomotion in legged robots enables them to overcome obstacles and navigate complex and unstructured terrain. However, the leg mechanisms and actuators needed for versatile locomotion are much more challenging to manufacture and integrate in sub‐gram scale robots. Herein, Picotaur, a 15.4 mg hexapedal robot with legs that enable various locomotion tasks such as turning, climbing 3D‐printed stairs, and pushing loads for the first time at these size scales, is presented. 3D printing with two‐photon polymerization enables the manufacture of electrostatically driven 2 degrees of freedom legs on a robot body made from a flexible printed circuit board. Based on simple control inputs, Picotaur can achieve alternating tripod gaits, reaching speeds up to 57 mm (7.2 body lengths) per second, as well as pronking gaits to tackle a wider variety of terrain. This approach to manufacturing and controlling legged robots at smaller scales provides a path forward toward robots that can be used for practical applications ranging from inspection to exploration and rival the performance of insects at similar size scales.

Revealing the inherent running mechanism of quadruped mammals based on a novel bionic stiffness model

In this paper, the limb of a goat is chosen as the research object, and according to mammalian anatomy, a bionic model called the quasi inverted pendulum with “J” curve spring (QIPJCS) model with nonlinear stiffness is built, and the equations of motion are derived. Based on these equations, the advantages of the QIPJCS model are illustrated from the aspect of the stable motion region by the SFA (step-to-fall analysis) numerical simulation method. These results are compared with the traditional SLIP model. Furthermore, the ARM (Apex-Return-Map) of this model is built, and the fixed points are analyzed. Finally, according to the locomotion law of goats running with gallop gaits and the analysis of the dead-point support effect, the dynamic motion mechanism of goat limbs is elucidated, and the equivalent mechanism model is built. Based on the mechanism, the dynamic mechanical analysis indicates that the joint driving torque can be minimized to conserve energy by optimizing the landing angle. The running mechanism research of quadruped mammals, which is based on the novel bionic stiffness model, provides theoretical support for the design of high-performance mechanical legs and the motion control of bionic robots.

Motion planning and contact force distribution for heavy‐duty hexapod robots walking on unknown rugged terrains

AbstractHeavy‐duty hexapod robots have impressive stability, high load‐bearing capacity, and exceptional adaptability to rugged terrains. They are capable of working in challenging outdoor environments such as planetary exploration, disaster relief and mountain transportation. Their ability to traverse terrain requires effective motion planning and accurate force distribution, neither of which is currently at the level required for widespread practical applications. In this paper, the mechanical legs are divided into support and swing legs, and the adaptability of the hexapod robot to unknown rugged terrain is enhanced by introducing the Decomposition Quadratic Programming‐based Contact Force Distribution (DQP‐based CFD) method. Moreover, an efficient replanning strategy can handle accidental collisions between swinging legs and unmodelled obstacles. Extensive field experiments demonstrate the effectiveness of our proposed motion planning and contact force distribution methods.

A Kinematics-Based Optimization Design for the Leg Mechanism of a Novel Earth Rover

Abstract This paper proposes a general kinematic-based design method for optimizing the side-mounted leg mechanism of BJTUBOT, a novel multi-mission quadrupedal Earth rover. The focus issue lies in designing structural improvements that not only enhance its kinematic performance but also prevent singularity, all while meeting the demands for miniaturization and lightweight without deviating from the original leg design concept. To solve this issue, a novel 3-UPRU&PPRR mechanism is envisaged based on the original configuration. Around the unique structural features of this mechanism, its inverse kinematic solution and Jacobian matrix are calculated, and a coupled motion relation between a key limb and its moving platform (MP) is presented. In order to achieve singularity avoidance, some typical singularity configurations based on line geometry analysis are given. In accordance with this result, an initial configuration for multi-objective dimensional optimization is presented. To further enhance its kinematic performance, we introduce the use of the GCI (global conditional index) performance at extreme positions as one of the optimization criteria based on the NSGA-II (Non-dominated Sorting Genetic Algorithm) algorithm, and directly measuring the crowding distance using the position vector of the U (universal) joints on the moving platform. This optimized mechanism prototype is demonstrated in a single-leg Adams simulation, which exhibits good velocity mapping effects and displacement accuracy. Finally, a new BJTUBOT prototype was constructed based on the optimized leg, and its flexibility was tested with various classical forms of motions. The workflow in this paper significantly improves the leg performance under the current design needs.

Design and Research on the Mechanical Structure of a Heavy-Duty Hexapod Robot with Bouncing Characteristics

Based on the lunar exploration project, a mechanical structure design scheme for a heavy-duty hexapod robot movement system with bounce characteristics was proposed. The materials used were determined by the robot's working environment and performance standards. The mechanical structure of a jumping heavy-duty hexapod robot was designed using SolidWorks 3D modeling software. Based on the analysis of the working modes of the root joint, hip joint, knee joint, and jumping energy storage mechanism, the main components of each joint and jumping energy storage mechanism were designed, and a single leg mechanism was obtained. Based on the special soil structure on the lunar surface, the foot end buffer mechanism was designed, and finite element stress analysis was conducted on the key components of the robot model, proving the rationality of the mechanical structure of a heavy-duty hexapod robot with bounce characteristics.

Design and verification of a parallel elastic robotic leg

This paper presents the design and experimental verification of a parallel elastic robotic leg mechanism that aims to capture the dynamics of the linear mass-spring-damper model. The mechanism utilizes a wrapping cam mechanism to linearize the non-linear force resulting from the elongation of the parallel elastic element. Firstly, we explain the desired dynamics of the mass-spring-damper model, including the impact transitions, and the design of the wrapping cam mechanism. We then introduce a system identification procedure to estimate the parameters of the leg mechanism corresponding to the dynamic model. The estimated parameters are tested with a cross-validation approach to evaluate the mechanism’s performance in tracking the desired model. The experimental results show that the passive dynamics of the mechanism resemble the linear model as intended. Thus, the robot provides a basis for using parallel elastic actuation while using model-based controllers that benefit the analytic solutions of the linear model.

Analysis of a network of FitzHugh-Nagumo neuron circuit coupled to an array of mechanical leg to mimic the locomotion of a multi-legged organism

A bioinspired electromechanical system that employs an array of FitzHugh–Nagumo (FN) neuron circuits designed to drive synchronically an array of mechanical legs is proposed in this paper. The schematic of the electromechanical device is transformed into an equivalent mathematical model thanks to Kirchhoff’s and Newton’s laws. The results of numerical simulations of the model generate an action potential (AP) that follows directly from the excitation of a single block of cell and does not propagate the signal in the neighboring blocks. When the stimulation time is lesser than 3-time units, the AP of the next block is generated during the repolarization of the previous cell, and the instantaneous displacement of the legs of the next block goes operational before the resting state of the previous block of the cell. For stimulation time greater than or equal to 3-time units, the AP is initiated just after the repolarization of the previous block of cells has terminated its activities and the instantaneous displacement of the leg of the next block goes operational, a direct consequence of neuron's communication without loss of amplitude in the permanent regime. Finally, straightforward motion without rotation is achieved.

Cognitive-motor interference during walking with modified leg mechanics: a dual-task walking study.

The use of mobile exoskeletons as assistive walking devices has the potential to affect the biomechanics of the musculoskeletal system due to their weight and restricted range of motion. This may result in physical and cognitive load for the user. Understanding how lower extremity loading affects cognitive-motor interference is crucial for the design of wearable devices, including powered exoskeletons, and the development of effective training interventions. This study aims to examine the effects of modified leg mechanics on cognitive-motor interference in dual-task walking. Gait variability, as an indicator of motor control, was analyzed to investigate its relation to cognitive task difficulty and to determine whether lower extremity loading modifies this relationship. Additionally, the impact on the gait pattern, as represented by the mean values of spatio-temporal gait parameters were investigated. Fifteen healthy young adults walked on a treadmill with and without weight cuffs bilaterally attached to their thighs and shanks while performing a visual-verbal Stroop test (simple task) and a serial subtraction task (difficult task). Dependent variables include mean values and variability (coefficients of variation) of step length, step width, stride time and double support time. Additionally, secondary task performance as correct response rates and perceived workload were assessed. Double support time variability decreased during dual-task walking, but not during walking with modified leg mechanics while performing the difficult secondary task. Walking with modified leg mechanics resulted in increased gait variability compared to normal walking, regardless of cognitive load. During walking with modified leg mechanics, step length, step width, and stride time increased, while double support time decreased. The secondary tasks did not affect the gait pattern. The interplay between an external focus of attention and competition for attentional resources may influence the variability of double support time. The findings suggest that walking with modified leg mechanics could increase cognitive-motor interference for healthy young adults in demanding dual-task situations. Therefore, it is important to analyze the underlying mechanisms of cognitive-motor interference in the context of human-exoskeleton interaction.

One-degree-of-freedom planar link leg mechanisms design without predetermined trajectory using a genetic algorithm

One-degree-of-freedom planar link leg mechanisms design without predetermined trajectory using a genetic algorithm

Leg Mechanism Design and Motion Performance Analysis for an Amphibious Crab-like Robot

Bionic-legged robots draw inspiration from animal locomotion methods and structures, demonstrating the potential to traverse irregular and unstructured environments. The ability of Portunus trituberculatus (Portunus) to run flexibly and quickly in amphibious environments inspires the design of systems and locomotion methods for amphibious robots. This research describes an amphibious crab-like robot based on Portunus and designs a parallel leg mechanism for the robot based on biological observations. The research creates the group and sequential gait commonly used in multiped robots combined with the form of the robot’s leg mechanism arrangement. This research designed the parallel leg mechanism and modeled its dynamics. Utilizing the outcomes of the dynamics modeling, we calculate the force and torque exerted on each joint of the leg mechanism during group gait and sequential gait when the robot is moving with a load. This analysis aims to assess the performance of the robot’s motion. Finally, a series of performance evaluation experiments are conducted on land and underwater, which show that the amphibious crab-like robot has good walking performance. The crab-like robot can perform forward, backward, left, and right walking well using group and sequential gaits. Simultaneously, the crab-like robot showcases faster movement in group gaits and a more substantial load capacity in sequential gaits.

A steerable robot walker driven by two actuators

Abstract This article describes a robot walker based on a new single degree-of-freedom six-bar leg mechanism that provides rectilinear, non-rotating, movement of the foot. The walker is statically stable and requires only two actuators, one for each side, to provide effective walking movement on a flat surface. We use Curvature Theory to design a four-bar linkage with a flat-sided coupler curve and then adds a translating link so that walker foot follows this coupler curve in rectilinear movement. A prototype walker was constructed that weighs 1.6 kg, is 180 mm tall, and travels at 162 mm/s. This is an innovative legged robot that has a simple reliable design.

Experimental investigation of relationship between bearing capacity and vibration parameters for planetary exploration legged rovers

In recent years, robots with leg mechanisms have received considerable attention as high-running planetary exploration rovers. Rovers undertaking planetary exploration require outstanding running performance to travel on loose ground on which they mostly slip and hardly move forward. The movement of the rover easily deforms the surface of loose ground. This problem can be solved by increasing the bearing capacity. The bearing capacity, the resistance force exerted on the rover legs when they make contact with the ground, needs to be sufficiently large to prevent legged rovers from slipping on loose ground. The bearing capacity can be increased by compaction of the ground by imparting vibrations. This study investigates the relationship between the bearing capacity in the horizontal direction and vibration parameters because this relationship offers valuable information for improving the running performance of legged rovers. First, we investigated the effect of changing the vibration parameters on the bearing capacity. Our experimental results show that the bearing capacity is related to vibration acceleration. These results suggest that the bearing capacity can be estimated from the vibration acceleration. Next, the frequency and amplitude were compared as vibration parameters to devise an efficient method for increasing the bearing capacity. The results of these experiments showed that high-amplitude vibrations increase the bearing capacity to a greater extent than high-frequency vibrations. The reason is that high-amplitude vibrations generate larger additional vibrations by the collision between the rod and the ground than high-frequency vibrations. This knowledge is valuable for selecting a suitable vibration that can efficiently increase the bearing capacity. This study suggests a method of facilitating further planetary exploration using legged rovers.

Structural design and jumping motion planning of the jumping leg inspired by a goat's hindlimb

Abstract. At present, research on bionic jumping robots mainly focuses on imitating various jumping animals, such as kangaroos, frogs, or locusts. These bionic objects have good jumping ability. The goat, as one of these with a moderate size and a strong jumping ability, is very suitable as a prototype to imitate jumping. In this study, first, a simplified serial joint model that imitates a goat's hindlimb is proposed with a comparison analysis of its physiological structure. Then, a jumping leg mechanism that imitates a goat's hindlimb was designed. Second, the kinematics of the goat-inspired jumping leg were constructed to describe the relationship between joint angles and foot positions. Additionally, we used a cubic polynomial to plan the trajectory of the jumping process to achieve a smooth jumping movement based on the characteristics of the goat's jumping, with position and speed constraints during the jump. Thus, we established a smooth jumping trajectory model of the goat-inspired jumping leg. Finally, experiments on the jumping of the goat-inspired jumping leg were conducted. The goat-inspired jumping leg has good jumping performance. In this study, we took the goat's hindlimbs as the bionic model, proposed the goat-inspired jumping leg mechanism, and presented the jumping trajectory planning theory for smooth jumping of the goat-inspired jumping leg. These provide new ideas for the study of bionic jumping legs and can effectively promote further development of bionic jumping robots.

Novel Robust Control Strategy for the Mechanical Legs of Lunar-Based Equipment

Novel Robust Control Strategy for the Mechanical Legs of Lunar-Based Equipment

Development of a model for a walking robot made of Desai mechanism using ANN and regression approach

The study focuses on computing the optimized foot profile for a walking leg mechanism using artificial neural network (ANN), genetic algorithm, and regression approaches. The technique adopted in this work is the benchmark approach and acts as a tool for complex problems. A mathematical model using regression and ANN is developed for the 8-link coplanar mechanism. Optimum link lengths are obtained to minimize the objective function (error). The output response is the foot length with a minimum foot height of 124 mm for obstacle clearance. A neural network is designed with seven neurons (one neuron/link) in the input layer. Optimum neurons in the hidden layer are determined based on the output obtained through simulation. A single neuron is used to represent the foot profile length at the output layer. The foot lengths obtained from the regression model and ANN are compared and validated with a genetic algorithm for the data sets of 100, 200, 300, 400, and 500. Simulation studies of the walking leg mechanism revealed a difference of 19%, 22.4%, and 5.23% in the foot profile by ANN and mathematical, ANN and regression model, and mathematical and regression approach respectively. This paper reveals that different approaches viz., ANN, mathematical and regression models generate dissimilar foot profiles.