Shin-Min Song

An analytical approach for gait study and its applications on wave gaits

In the past, the determination of the gait stability margins of legged locomotion systems depended mainly on numerical computation assisted by graphical methods. Although some of these results were expressed as empirically derived equa tions, analytical derivations were lacking. The only exception was the equation of the longitudinal stability margin for quadruped wave gaits derived by McGhee and Frank (1968). They applied a complicated, nonlinear programming ap proach to the derivation. In this paper, we describe an ana lytical approach that has proved to be more efficient than previous gait study techniques. This analytical approach de fines the foot positions by means of the concept of local phase, which is the fraction of a cycle period by which the current foot position follows the placement of that foot. Based on this concept, basic theorems that simplify the study of periodic gaits are developed. This analytical approach is then applied to derive a general equation for the longitudinal stability margin for the 2n-legged wave gait. Also, this ap proach is applied to study the effects on the stability margin of the wave gait by varying the stroke and the pitch of the leg.

An efficient method for inverse dynamics of manipulators based on the virtual work principle

The computational efficiency of inverse dynamics of a manipulator is important to the real-time control of the system. For serial manipulators, the recursive Newton-Euler method has been proven to be the most efficient. However, for more general manipulators, such as serial manipulators with closed kinematic loops or parallel manipulators, it must be modified accordingly and the resultant computational efficiency is degraded. This article presents a computationally efficient scheme based on the virtual work principle for inverse dynamics of general manipulators. The present method uses a forward recursive scheme to compute velocities and accelerations, the Newton-Euler equation to calculate inertia forces/torque, and the virtual work principle to formulate the dynamic equations of motion. This method is equally effective for serial and parallel manipulators. For serial manipulators, its computational efficiency is comparable to the recursive Newton-Euler method. For parallel manipulators or serial manipulators with closed kinematic loops, it is more efficient than the existing methods. As an example, the computations of inverse dynamics (including inverse kinematics) of a general Stewart platform require only 842 multiplications, 511 additions, and 12 square roots.

Forward kinematics of a class of parallel (Stewart) platforms with closed‐form solutions

This article studies the geometrical condition for closed-form solutions of forward kinematics of parallel platforms. It is shown that closed-form solutions are available if 1 rotational degree of freedom (dof) of the moving platform is decoupled from the other 5 dof. Geometrically, this condition is satisfied when five end-points at the moving platform (or at the base) are colinear. A general case that these five points do not coincide with each other is studied first and is shown to have 16 possible closed-form solutions. The variations of parallel platforms that satisfy the above-mentioned geometrical condition are then discussed. Some of them have the additional feature that the three rotational dof are fully decoupled from the 3 translational dof and their closed-form solutions are further simplified. One particular case has extremely simple forward kinematics and could be used as an alternative to the Stewart platform.

Computer-aided design of a leg for an energy efficient walking machine

Abstract Vehicles with legs instead of wheels have been studied for a number of years. One of the reasons for interest in such vehicles is that animals use only 10% as much energy as wheeled or tracked vehicles when traveling over rough terrain. The leg geometry is the most crucial aspect of the design since it strongly influences the efficiency of the vehicle. The legs should be simple in structure, and when the motion of the body is on a horizontal straight line, only one actuator per leg should be active in order to have good energy efficiency. The design of an energy efficient walking machine leg is described in this paper. In the design procedure, the motion of the leg is considered first, and a very simple leg developed from a 4-bar linkage and designed using a computer-aided interactive program is described. Second, the forces on this leg during a typical motion cycle are discussed. The leg is driven by a primary actuator for straight line walking and two secondary actuators which vary working height and change direction. A prototype of the leg is being built in The Department of Mechanical Engineering at The Ohio State University.

Path planning and gait of walking machine in an obstacle‐strewn environment

The locomotion of a quadrupedal walking machine in an obstacle-strewn environment is studied. The path planning of the walking machine body includes the following two features : first, the path is generated based on the Bezier curve so that its shape can be easily adjusted to avoid obstacles ; second, the velocity and acceleration are assigned independently from the path generation so that the inertial terms are controllable. After the path has been generated, a gait algorithm that enables the walking machine to follow the path and maintain stability is developed. Two special cases―straight-line crab walking and turning about a fixed axis―are studied first. The general case that the walking machine is following an arbitrary curve is then studied. During walking, if the crab angle exceeds a certain limit, the gait needs to be changed in order to maintain stability. The methods for changing the gaits are discussed

Computer-Aided Geometric Design of Legs for a Walking Vehicle

Abstract A legged vehicle is potentially more energy efficient and mobile than conventional vehicles in rough terrain. The performance of such a legged vehicle is strongly dependent on the leg geometry. In general, a leg linkage which possesses three-degree-of-freedom foot motion is adequate. A preliminary design of the leg with a view to good energy efficiency resulted in a four-bar leg. This was described by S. M. Song et al. [Mech. Mach. Theory19, 17–24 (1984)]. In the present paper, the mobility of the legged vehicle is brought into consideration in the leg design. A study of the mobility of a six-legged vehicle shows that a large walking envelope is required for each leg linkage. In order to satisfy this requirement, the original four-bar leg was modified into a seven-bar leg by mounting another four-bar linkage on the coupler of the original four-bar linkage. Also, a different type of leg linkage based on pantograph mechanism was designed. A comparison of the leg performance of both types of leg is made in this paper and the pantograph leg is found to be more effective.

A Study of Reactional Force Compensation Based on Three-Degree-of Freedom Parallel Platforms

Reaction compensation is necessary for space robot applications because reactional forces/torques will cause undesired movement of the spacecraft. Because the reactional torques can be compensated by the existing torque balancing device in the spacecraft, an additional reaction compensating device is necessary to compensate the reactional forces. In this article we study two types of reactional force compensating devices based on three-degree-of freedom, parallel platforms. The first type has three R-P-S legs while the second type has three R-R-P-S leg and a passive R-R-P leg. A three-degree of freedom serial manipulator is used to generate reactional forces, which are to be compensated by the paralle platforms. The kinematics and dynamics of both platforms are analyzed and closed form inverse kinematics solutions are derived. We then design a reactional force compensating device that satisfies the strict volume constraint in a spacecraft. The first type of parallel platform is found to require very long legs due to large orientational motion at certain positions. The second type has smooth motion in both position and orientation, and therefore its size can be very compact. It is concluded that the second type of parallel platform has great potential to be used as a compact reactional force compensating device.

Motion study of two- and three-dimensional pantograph mechanisms

Abstract Coupling of vertical, horizontal and rotory motions in manipulators slows down calculating speed for real time control and lowers system energy efficiency. Pantograph mechanisms can be, and are being used as manipulators to remove the coupling of motion. In this paper, the basic theorems and equations of both two- and three-dimensional pantograph mechanisms are presented. The motion characteristics and singularities of the pantograph are also discussed. Methods which are used to determine the workspaces of pantograph type manipulators are developed and illustrated in an example. Some aspects of structural design of these pantographs are also discussed.

Mechanical and Geometric Design of the Adaptive Suspension Vehicle

Some aspects of the mechanical and geometric design of the adaptive suspension vehicle are presented. In particular, there is an emphasis on aspects of the leg design and vehicle geometry, which affect the ability of the vehicle to operate on steep grades or to cross obstacles. A mechanism that maintains the attitude of the foot approximately parallel to the body is described. Geometric aspects of maintaining static stability on steep grades are discussed. Geometric and gait sequence aspects of crossing severe obstacles are also discussed.

Forward kinematics of walking machines with pantograph legs based on selections of independent joints

This article studies the forward kinematics of walking machines with pantograph legs. The walking machine is supported by three legs and each leg has 3 degrees of freedom (dof). Because the body has 6 dof motion, only 6 joint variables among the 9 are independent. Thus, there are 84 possible ways to select the 6 independent joint variables. It is shown that the complexity of the forward position solutions is very much dependent on the selection of independent joints. In the category of 3:2:1 (the 3 numbers denote the number of independent joints at each of the supporting legs), all 54 combinations give closed-form solutions. Among the 27 combinations of category 2:2:2, 10 possess closed-form solutions, 16 yield to higher-order polynomials, and 1 gives no solutions. The 3 combinations of category 3:3:0 give no solutions. The results are useful to control and simulation of walking machines and other parallel systems consisting of pantograph subchains such as parallel manipulators, multifingered hands, and multiply coordinated manipulators.