Recent literature on walking robots deals predominantly with multi-degrees-of-freedom leg mechanisms and machines capable of adopting several gaits.This paper explores the other end of the spectrum suggesting mechanis...Recent literature on walking robots deals predominantly with multi-degrees-of-freedom leg mechanisms and machines capable of adopting several gaits.This paper explores the other end of the spectrum suggesting mechanisms derived from a four bar coupler curve for a one degree of freedom walking robot.Simulation of the walk indicates that body of the robot is able to move with low variation in velocity.The best strategy for changing the gait to enable the robot to walk over obstacles and the effect of change in length of different links are explored to open up the possibility of a two degree of freedom walking robot with the capability of changing its gait,suitable as a low cost unit for several applications.Such rugged units would permit the use of an IC engine as the primary source of power and could be of utility in installations where electronics may not be functional.In simple walking machines the foot of a leg is usually required to trace a D shaped curve with respect to the chassis.In this paper we begin with a Hoecken mechanism capable of tracing such a curve.The foot is required to move parallel to itself and the same could be achieved using a six or eight link mechanism.A few such devices have been synthesized in this paper and their motion properties compared.The study also covers the possibility of providing adjustments to vary the step length and height of the foot＇s movement.展开更多
This paper presents two new families of the generalized Ball curves which include the Be ′zier curve, the generalized Ball curves defined by Wang and Said independently and some intermediate curves. The relati...This paper presents two new families of the generalized Ball curves which include the Be ′zier curve, the generalized Ball curves defined by Wang and Said independently and some intermediate curves. The relative degree elevation and reduction schemes, recursive algorithms and the Bernstein\|Be ′zier representation are also given.展开更多
A DP curve is a new kind of parametric curve defined by Delgado and Pefla(2003);it has very good properties when used in both geometry and algebra,i.e.,it is shape preserving and has a linear time complexity for evalu...A DP curve is a new kind of parametric curve defined by Delgado and Pefla(2003);it has very good properties when used in both geometry and algebra,i.e.,it is shape preserving and has a linear time complexity for evaluation.It overcomes the disadvantage of some generalized Ball curves that are fast for evaluation but cannot preserve shape,and the disadvantage of the Bézier curve that is shape preserving but slow for evaluation.It also has potential applications in computer-aided design and manufacturing(CAD/CAM) systems.As conic section is often used in shape design,this paper deduces the necessary and sufficient conditions for rational cubic or quartic DP representation of conics to expand the application area of DP curves.The main idea is based on the transformation relationship between low degree DP basis and Bernstein basis,and the representation theory of conics in rational low degree Bézier form.The results can identify whether a rational low degree DP curve is a conic section and also express a given conic section in rational low degree DP form,i.e.,give positions of the control points and values of the weights of rational cubic or quartic DP conics.Finally,several numerical examples are presented to validate the effectiveness of the method.展开更多
文摘Recent literature on walking robots deals predominantly with multi-degrees-of-freedom leg mechanisms and machines capable of adopting several gaits.This paper explores the other end of the spectrum suggesting mechanisms derived from a four bar coupler curve for a one degree of freedom walking robot.Simulation of the walk indicates that body of the robot is able to move with low variation in velocity.The best strategy for changing the gait to enable the robot to walk over obstacles and the effect of change in length of different links are explored to open up the possibility of a two degree of freedom walking robot with the capability of changing its gait,suitable as a low cost unit for several applications.Such rugged units would permit the use of an IC engine as the primary source of power and could be of utility in installations where electronics may not be functional.In simple walking machines the foot of a leg is usually required to trace a D shaped curve with respect to the chassis.In this paper we begin with a Hoecken mechanism capable of tracing such a curve.The foot is required to move parallel to itself and the same could be achieved using a six or eight link mechanism.A few such devices have been synthesized in this paper and their motion properties compared.The study also covers the possibility of providing adjustments to vary the step length and height of the foot＇s movement.
文摘This paper presents two new families of the generalized Ball curves which include the Be ′zier curve, the generalized Ball curves defined by Wang and Said independently and some intermediate curves. The relative degree elevation and reduction schemes, recursive algorithms and the Bernstein\|Be ′zier representation are also given.
基金supported by the National Natural Science Foundation of China (Nos.60873111 and 60933007)the Natural Science Foundation of Zhejiang Province,China (No.Y6090211)
文摘A DP curve is a new kind of parametric curve defined by Delgado and Pefla(2003);it has very good properties when used in both geometry and algebra,i.e.,it is shape preserving and has a linear time complexity for evaluation.It overcomes the disadvantage of some generalized Ball curves that are fast for evaluation but cannot preserve shape,and the disadvantage of the Bézier curve that is shape preserving but slow for evaluation.It also has potential applications in computer-aided design and manufacturing(CAD/CAM) systems.As conic section is often used in shape design,this paper deduces the necessary and sufficient conditions for rational cubic or quartic DP representation of conics to expand the application area of DP curves.The main idea is based on the transformation relationship between low degree DP basis and Bernstein basis,and the representation theory of conics in rational low degree Bézier form.The results can identify whether a rational low degree DP curve is a conic section and also express a given conic section in rational low degree DP form,i.e.,give positions of the control points and values of the weights of rational cubic or quartic DP conics.Finally,several numerical examples are presented to validate the effectiveness of the method.
