Leg Mechanism Research Articles

Robotic Modular Leg: Design, Analysis, and Experimentation

This paper presents the design and analysis of a reduced degree-of-freedom (DOF) robotic modular leg (RML) mechanism. The RML is composed of a two serially connected four-bar mechanisms that utilize mechanical constraints between articulations to maintain a parallel orientation between the foot and body without the use of an actuated ankle. Kinematic and dynamic models are developed for the leg mechanism and used to analyze actuation requirements and aid motor selection. Experimental results of an integrated prototype tracking a desired foot trajectory are analyzed to improve the accuracy and repeatability of the mechanism. The prototype weighs 4.7 kg and measures 368 mm in a fully extended configuration and exhibits a maximum deviation from the straight line support phase equivalent to 5.2 mm.

Characterization of frictional multi-legged equilibrium postures on uneven terrains

Quasistatic legged locomotion over uneven terrains requires characterization of the legged robot equilibrium postures as well as an understanding of the non-static motion modes that can develop at the contacts. This paper characterizes the frictional multi-legged equilibrium postures on a generic class called ‘tame stances’, which satisfy a generalized support polygon principle. To characterize the equilibrium postures, the paper lumps the legged mechanism’s kinematic structure into a rigid body having a variable center of mass and maintaining the same contacts with the terrain. The equilibrium postures associated with a given set of contacts correspond to the locations of the center of mass at which the body is supported in static equilibrium by the same contacts under the influence of gravity. This paper thus characterizes the feasible equilibrium region of a rigid body having a variable center of mass and supported by multiple frictional contacts under the influence of gravity. The paper establishes that the feasible equilibrium region forms a convex set which has five types of boundary curves. These boundary curves are formulated analytically, illustrated with graphical examples, and associated with the onset of five non-static motion modes at the contacts. The paper also compares the analytical results against experimental measurements conducted on a legged mechanism prototype.

Singularity Analysis and Dimensional Optimization on a Novel Serial-parallel Leg Mechanism

A novel series-parallel hybrid mechanism is presented to overcome the limitations of serial robots and parallel robots caused by the mechanism characteristics, and using it as the leg, a serial-parallel quadruped robot is structured. Based on vector method and differential transform method, velocity Jacobian matrix of the hybrid leg mechanism is gained, and singularity of the leg is analyzed ulteriorly. In order to evaluate the kinematic dexterity of the hybrid leg, dexterity evaluation indexDh is proposed, further more, dimensional optimization has been taken according to index Dh, and results show that, when angle between driving shaft of the hip and vertical direction is 50.5 degree and the ratio of the thigh and the calf is 0.72, index Dh is maximum, that is, the hybrid leg has best dexterity. In accordance with the results of the optimization, prototypes of the hybrid leg and the serial-parallel quadruped walking robot have been successfully trial-produced. This research helps lay a solid foundation for a series of further studies of the novel series-parallel quadruped robots.

Walk Control of a Centipede Type Legged Robot Composed of 1-DOF Leg Mechanism Units Serially Connected with Passive Joints

Walk Control of a Centipede Type Legged Robot Composed of 1-DOF Leg Mechanism Units Serially Connected with Passive Joints

Analysis and Experiment on the Steering Control of a Water-running Robot Using Hydrodynamic Forces

Steering is important for the high maneuverability of mobile robots. Many studies have been performed to improve the maneuverability using a tail. The aim of this research was to verify the performance of a water-running robot steering on water using a tail. Kinematic analysis was performed for the leg mechanism and the interaction forces between the water and the feet to calculate the propulsive drag force of the water. This paper suggests a simplified planar two-link rigid body model to determine the dynamic performance of the robotic platform with respect to the effect of the tail's motion. Simulations based on a dynamic model were performed by applying a range of motions to the tail. In addition, a simulation with a Bang-bang controller was also performed to control the main frame's yawing locomotion. Finally, an experiment was conducted with the controller, and the simulation and experimental results were compared. These results can be used as a guideline to develop a steerable water-running robot.

Design Exploration and Kinematic Tuning of a Power Modulating Jumping Monopod

The leg mechanism of the novel jumping robot, Salto, is designed to achieve multiple functions during the sub-200 ms time span that the leg interacts with the ground, including minimizing impulse loading, balancing angular momentum, and manipulating power output of the robot's series-elastic actuator. This is all accomplished passively with a single degree-of-freedom linkage that has a coupled, unintuitive design which was synthesized using the technique described in this paper. Power delivered through the mechanism is increased beyond the motor's limit by using variable mechanical advantage to modulate energy storage and release in a series-elastic actuator. This power modulating behavior may enable high amplitude, high frequency jumps. We aim to achieve all required behaviors with a linkage composed only of revolute joints, simplifying the robot's hardware but necessitating a complex design procedure since there are no pre-existing solutions. The synthesis procedure has two phases: (1) design exploration to initially compile linkage candidates, and (2) kinematic tuning to incorporate power modulating characteristics and ensure an impulse-limited, rotation-free jump motion. The final design is an eight-bar linkage with a stroke greater than half the robot's total height that produces a simulated maximum jump power 3.6 times greater than its motor's limit. A 0.27 m tall prototype is shown to exhibit minimal pitch rotations during meter high test jumps.

Robotic vertical jumping agility via series-elastic power modulation.

Several arboreal mammals have the ability to rapidly and repeatedly jump vertical distances of 2 m, starting from rest. We characterize this performance by a metric we call vertical jumping agility. Through basic kinetic relations, we show that this agility metric is fundamentally constrained by available actuator power. Although rapid high jumping is an important performance characteristic, the ability to control forces during stance also appears critical for sophisticated behaviors. The animal with the highest vertical jumping agility, the galago (Galago senegalensis), is known to use a power-modulating strategy to obtain higher peak power than that of muscle alone. Few previous robots have used series-elastic power modulation (achieved by combining series-elastic actuation with variable mechanical advantage), and because of motor power limits, the best current robot has a vertical jumping agility of only 55% of a galago. Through use of a specialized leg mechanism designed to enhance power modulation, we constructed a jumping robot that achieved 78% of the vertical jumping agility of a galago. Agile robots can explore venues of locomotion that were not previously attainable. We demonstrate this with a wall jump, where the robot leaps from the floor to a wall and then springs off the wall to reach a net height that is greater than that accessible by a single jump. Our results show that series-elastic power modulation is an actuation strategy that enables a clade of vertically agile robots.

Position model computational complexity of walking robot with different parallel leg mechanism topology patterns

This article studies computational complexity of kinematic models for 2 patterns of 1UP-2UPS parallel mechanisms. These mechanisms are designed for hexapod walking robots applying real time control systems, which require the computing speed of kinematic models to be as swift as possible. The difference of these 2 patterns is that rotational axes of universal joints on limb 1 are reversed. In this paper, both forward and inverse kinematic models are formulated and it will be shown that both pattern I and II have analytical solutions for inverse kinematic problems. However, the forward models can be derived to univariate polynomial equations with different orders: 8th for pattern I and 4th for pattern II. It is known that the highest degree of polynomials can be solved analytically is 4, thus the computational complexity of pattern I is much higher than pattern II. In our prototypes, the forward kinematic model of pattern I costs 10 times more time than pattern II, hence pattern II is preferred for mobile robots.

Kinematics Analysis of a Leg Mechanism as a Motion Converter

This paper presents kinematics analysis of a leg mechanism for converting linear motion into rotary motion to be used as a Regenerative Shock Absorber (RSA). The kinematics analysis determines the positions, the velocities and the accelerations when a leg mechanism is subjected to a linearly reciprocating motion. The main objectives of this paper are to obtain valid mathematical models and to figure out the ability of the mechanism converting motion. The work carried out in this paper includes deriving and analyzing mathematical model using analytical kinematics. A numerical simulation is used to show the response of the mathematical models. The validation is performed by comparing the result from kinematic simulation software and numerical simulation of the mathematical models. The performance of a leg mechanism is evaluated under sinusoidal displacement input for typical amplitudes and frequencies. The validation results show that the proposed mathematical models are generally valid. Moreover, the mechanism can convert 0.04 m of linear motion into 116.84° of rotation motion.

BRAIN-COMPUTER INTERFACE FOR THE AUGMENTATION OF BRAIN FUNCTIONS

Brain-computer interface (BCI) connects the nervous system departments with external devices for the purpose of recovery of motor and sensory functions of patients with neurological lesions. Over the past half-century BCI have gone from initial ideas to the high-tech modern incarnations. This development contributed significantly to the invasive techniques of multichannel registration activity of neuronal ensembles. Modern BCI are able to manage mechanical prosthetic arms and legs. Furthermore, BCI can provide sensory feedback, allowing the user to feel the movement of the prosthesis and its interaction with external objects. Latest BCI connect multiple users to the brain network. In this review, these achievements are dealt with a focus on invasive BCI.

Adaptation Behavior of Skilled Infant Bouncers: Leg Movements and Mechanisms of Control.

Rhythmic behavior in nonlinear systems can be described as limit cycles or attractors. System perturbations may result in shifts between multiple attractors. We investigated individual cycle-to-cycle leg movement kinematics of three prewalking skilled infant bouncers (10.6 ±0.91 months) during four different spring frequencies (0.9, 1.15, 1.27 and 1.56 Hz). A novel visual analysis phase-plane methodology was introduced to analyze the lower body joint kinematics. It was found that as infants' bounce frequency increased to match the natural frequency of the system, their joint ranges of motion decreased and lower extremity dynamics shifted from forced to simple harmonic motion. All infants produced highly synchronized and coordinated movements, as supported by moderate to high inter- and intralimb correlations. This study extends from previous work (Habib Perez et al., 2015) by focusing on the lower extremity kinematic movements, joint coordination and the occurrence of different movement patterns for individual bounce cycles over four spring conditions.

Dimensional synthesis of a leg mechanism

An eight bar leg mechanism dimensional synthesis is presented. The mathematical model regarding the synthesis is described and the results obtained after computation are verified with help of 2D mechanism simulation in Matlab. This mechanism, inspired from proposed solution of Theo Jansen, is integrated into the structure of a 2 DOF quadruped robot. With help of the kinematic synthesis method described, it is tried to determine new dimensions for the mechanism, based on a set of initial conditions. These are established by taking into account the movement of the end point of the leg mechanism, which enters in contact with the ground, during walking. An optimization process based on the results obtained can be conducted further in order to find a better solution for the leg mechanism.

A feasibility study on the design and walking operation of a biped locomotor via dynamic simulation

A feasibility study on the mechanical design and walking operation of a Cassino biped locomotor is presented in this paper. The biped locomotor consists of two identical 3 degrees-of-freedom tripod leg mechanisms with a parallel manipulator architecture. Planning of the biped walking gait is performed by coordinating the motions of the two leg mechanisms and waist. A threedimensional model is elaborated in SolidWorks® environment in order to characterize a feasible mechanical design. Dynamic simulation is carried out in MSC.ADAMS® environment with the aims of characterizing and evaluating the dynamic walking performance of the proposed design. Simulation results show that the proposed biped locomotor with proper input motions of linear actuators performs practical and feasible walking on flat surfaces with limited actuation and reaction forces between its feet and the ground. A preliminary prototype of the biped locomotor is built for the purpose of evaluating the operation performance of the biped walking gait of the proposed locomotor.

Six Links Passive Modular Group Applied to the Inverse Structural Model of the Bi-Mobile Leg Mechanisms

The structural synthesis of bi-mobile mechanisms has some particularities. The effector of such systems must have the motion dependent on two independent parameters, the selection of the basis and the effector in the linkage being made through the inverse structural model. The active pair placement in the linkage is imposed by the conditions settled to the system by its direct structural model. Due to the theoretical difficulties of mathematical models the passive complex modules with six links are rarely met in construction and design of mechanisms. The relevance of the paper is given by the possibility to create new original structures applying six links passive modular groups.

Design and optimization of a dual quadruped vehicle based on whole close-chain mechanism

A new “whole close-chain mechanism” concept is proposed for the design of the modular legged unit of walking vehicles. Based on this concept, the walking vehicle called dual quadruped vehicle is developed and constructed. The vehicle designed as an omnidirectional carrying platform contains two identical single-driven quadruped mechanisms. The details of the design procedure are given, including the single close-chain legged mechanism, the modular legged unit, and the dual quadruped vehicle. The construction description of the single leg is presented. With the optimum design of the whole close-chain legged mechanism, the two foot-point characteristic trajectories are investigated. Based on the strategies of the legged module integration, the best phase configuration in pitching movement and the steering analysis are discussed and illustrated. Dynamic simulations and experiments are performed to verify the validity of the theoretical analysis of the new concept and the maneuverability of the vehicle prototype.

Climbing Robot Design and Mechanism: A Review

This paper presents a survey on robot design and mechanism for climbing robots. The climbing robots are designed by engineers and scientists to conduct inspection on the cabling system, piping system and also for educational purposes. The robots design are utilizing either electrical actuator such as Direct Current (DC) motors, pneumatic actuators or mechanical legs for their movement. The controller to control the movement of the robots are varies from small microprocessor, personal computer or specialized built processor. These climbing robotic systems are crucial to be used inside high risk environments which cannot be accessed by human.

Method for six-legged robot stepping on obstacles by indirect force estimation

Adaptive gaits for legged robots often requires force sensors installed on foot-tips, however impact, temperature or humidity can affect or even damage those sensors. Efforts have been made to realize indirect force estimation on the legged robots using leg structures based on planar mechanisms. Robot Octopus III is a six-legged robot using spatial parallel mechanism(UP-2UPS) legs. This paper proposed a novel method to realize indirect force estimation on walking robot based on a spatial parallel mechanism. The direct kinematics model and the inverse kinematics model are established. The force Jacobian matrix is derived based on the kinematics model. Thus, the indirect force estimation model is established. Then, the relation between the output torques of the three motors installed on one leg to the external force exerted on the foot tip is described. Furthermore, an adaptive tripod static gait is designed. The robot alters its leg trajectory to step on obstacles by using the proposed adaptive gait. Both the indirect force estimation model and the adaptive gait are implemented and optimized in a real time control system. An experiment is carried out to validate the indirect force estimation model. The adaptive gait is tested in another experiment. Experiment results show that the robot can successfully step on a 0.2 m-high obstacle. This paper proposes a novel method to overcome obstacles for the six-legged robot using spatial parallel mechanism legs and to avoid installing the electric force sensors in harsh environment of the robot’s foot tips.

A compact stair-climbing wheelchair with two 3-DOF legs and a 1-DOF base

Purpose– The purpose of this paper is to describe a compact wheelchair, which has two 3-degrees of freedom (DOF) legs and a 1-DOF base (the total DOF of the leg system is 7) for stair-climbing, and wheels for flat surface driving.Design/methodology/approach– The proposed wheelchair climbs stairs using the two 3-DOF legs with boomerang-shaped feet. The leg mechanisms are folded into the compact wheelchair body when the wheelchair moves over flat surfaces. The authors also propose a simple estimation method of stair shape using laser distance sensors, and a dual motor driving system to increase joint power.Findings– The proposed wheelchair can climb arbitrary height and width stairs by itself, even when they are slightly curved. During climbing, the trajectory of the seat position is linear to guarantee the comfort of rider, and the wheelchair always keeps a stable condition to ensure the stability in an emergency stop.Originality/value– The wheelchair mechanism with foldable legs and driving wheels enables smooth stair climbing, efficient flat surface driving and additional useful motions such as standing and tilting.

Maximum-speed curve-running biomechanics of sprinters with and without unilateral leg amputations.

On curves, non-amputees' maximum running speed is slower on smaller radii and thought to be limited by the inside leg's mechanics. Similar speed decreases would be expected for non-amputees in both counterclockwise and clockwise directions because they have symmetric legs. However, sprinters with unilateral leg amputation have asymmetric legs, which may differentially affect curve-running performance and Paralympic competitions. To investigate this and understand the biomechanical basis of curve running, we compared maximum curve-running (radius 17.2 m) performance and stride kinematics of six non-amputee sprinters and 11 sprinters with a transtibial amputation. Subjects performed randomized, counterbalanced trials: two straight, two counterclockwise curves and two clockwise curves. Non-amputees and sprinters with an amputation all ran slower on curves compared with straight running, but with different kinematics. Non-amputees ran 1.9% slower clockwise compared with counterclockwise (P<0.05). Sprinters with an amputation ran 3.9% slower with their affected leg on the inside compared with the outside of the curve (P<0.05). Non-amputees reduced stride length and frequency in both curve directions compared with straight running. Sprinters with an amputation also reduced stride length in both curve-running directions, but reduced stride frequency only on curves with the affected leg on the inside. During curve running, non-amputees and athletes with an amputation had longer contact times with their inside compared with their outside leg, suggesting that the inside leg limits performance. For sprinters with an amputation, the prolonged contact times of the affected versus unaffected leg seem to limit maximum running speed during both straight running and running on curves with the affected leg on the inside.

Comparative study of leg mechanisms for fast and stable water-running

Bio-inspired water-running robots are widely researched for fast and energy-efficient locomotion on water surfaces. The leg mechanism is very important for achieving fast and stable cyclic motion locomotion of the footpads. In this paper, four-bar, Klann, and Watt-I leg mechanisms are compared for water-running robotic platforms. Each mechanism was compared using many groups of random variables to achieve the best performance for fast and stable water running. Many solutions for composing each mechanism were obtained based on random variables that satisfy constraint conditions. Kinematical analysis of the mechanisms was then conducted using the random variables. The four-bar and Klann mechanisms showed better performance for generating propulsion. The lifting forces were similar among the three mechanisms. The results can be a guideline for choosing mechanisms for water-running robots.