Conditions of crank existence for a particular case of the RSSR linkage

Necessary and sufficient conditions of motion transfer for a particular case of the RSSR linkage is further derived and simplified. This particular case is considered when the frame is coincided with input and output axes distance, which may also be called as “simply skewed form” of RSSR. The results show that the conditions of crank existence for this particular case can be represented in a way quite resembling the Grashof criterion applicable to planar four bar linkages, and thus are of very simple expression and geometric sense. (The term “simple” normally implies that overhand computation by “rigours” programming may not be needed.)     

三自由度并联机器人机构运动极限位置的精确解法

三自由度平面八杆机构，将其中两个原动件固定时，就成为Stephenson形平面六杆机构。该机构的输入输出角位移关系可用六次方程式来表示。因此，可用第1原动件的运动极限位移来取代六次方程式的重根，提出的这一方法同样适用于第2、第3原动件，此方法为三自由度平面八杆机构传动性能的评价指标提供了新的依据。     

Synthesis of adjustable planar 4-bar mechanisms

The ability of planar 4-bar mechanism, to generate various kinds of motion, can be greatly enhanced if it is made adjustable. With a simple adjustment of the position of the driven crank fixed pivot(s), a variety of outputs can be obtained with the same set of hardware.

This paper outlines synthesis techniques for 4-bar linkages, having adjustable driven crank pivots, for different motion generation problems. For a 4-bar mechanism, no more than five design positions can be specified. All the possible maximal motion specifications for the two “phases”, consisting of different combination of the five positions, are enumerated. This leads to four classes of motion generation problems. Synthesis procedure for each class is presented. An example of the P₁-P₂-P₃:P₁-P₄-P₅ case is solved. The method of solution is analytical in nature, and, therefore well suited for use on a digital computer.     

The analysis of planar linkages using a modular approachAnalyse des mecanismes plans par approche modulaire

Most complex planar linkages with lower pairs are actually made up of several simple mechanism components in series. When this is the case, it is possible to analyze the complex linkages by sequentially analyzing each of the simpler mechanism components. This procedure was described by Suh and Radcliffe[1], who have developed positive, velocity and acceleration equations for the component modules: rigid body, oscillating slider, two-link dyad, and rotating guide. The mechanism input module must be a driving crank.In this paper, this kinematic analysis technique is extended by incorporating dual slider, slider-crank, and inverted slider-crank modules, permitting mechanisms to be analyzed when a slider input, e.g. hydraulic or pneumatic cylinder, is involved.With this extension, most of the common compound planar mechanisms with lower pairs can be analyzed. However, there is still a class of mechanisms which cannot be analyzed in a direct fashion using the modular approach. These are mechanisms, such as the Watt “walking beam”, with more than two links between the moving end of the driver link and the frame. Such mechanisms can be analyzed using an inversion technique developed by Goodman[2], however; and the use of this technique with the modular technique is also discussed.The procedure developed is noniterative in nature and therefore can be conveniently programmed and executed on a minicomputer.     

Determination of Christoffel symbols of the first kind for a class of rigid body systems by topological considerations

The process of derivation of the equations of motion of a system of interconnected rigid bodies is often extremely laborious. In this paper, a method is presented in which the coefficients (Christoffel symbols) in the equations of motion of such a system may be derived in a straightforward manner. The method is developed in the context of planar systems of “tree structure”, but the principles may be extended to more difficult cases.     

用计算机几何技术求解多自由度平面机构的运动

综合采用计算机辅助几何约束、尺寸约束、尺寸方程和尺寸驱动技术，构造一些典型的多自由度平面连杆模拟机构。给定每个输入件的驱动尺寸，确定输出件被驱动尺寸，求解输出运动杆件位姿。利用CAD软件的记录功能，得到机构输出杆件位姿数据。用Excel软件拟合位姿数据，得到每个输入件驱动尺寸与输出件被驱动尺寸位姿拟合曲线和拟合方程。求解了机构输出件的速度和加速度方程。计算机模拟结果表明，该方法简捷直观、求解精度高、重复性好，而且可以完成复杂机构和多自由度机构的运动分析，为机器人和复合运动机构的运动分析提供更有效的工具。     

Simultaneous control of the motion and stiffness of redundant closed-loop link mechanisms with elastic elements

This paper describes the position and stiffness control of planar redundant link mechanisms with elastic elements in order to utilize the flexibility of robots. Assigning both of the two-dimensional position and stiffness of an output link as an output vector, the procedure of the forward kineto-static analysis for the planar redundant link mechanisms with elastic elements is formulated. The mechanisms have elastic linearactuators composed of a coil spring and linearactuator and rotary actuators and multi jointed links. An inverse kineto-static analysis to obtain the optimum input motions which can generate the desired position and stiffness of the output link while taking into account the motion range of the linearactuator is also conducted and applied to the optimum motion control of the mechanism. Several simulations and experiments with a prototype of a planar closed-loop manipulator with 5 DOF and 4 output show the effectiveness of the proposed method.     

On the modeling and composite control of flexible parallel mechanism

One of the key problems in high speed motion control of a flexible parallel mechanism (PM) is to damp out the mechanical vibration arising from high inertial force acting on the linkages and other components. In this paper, the dynamic equations of a 2 degree-of-freedom (DOF) planar PM with flexible links are established by taking the singular perturbation approach (SPA). Thus the model of the mechanism can be separated into slow time-scale and fast time-scale subsystems. Based on the feedback linearization theory and input shaping technique, the large range rigid motion controller and the flexible link vibration controller can be designed separately. A composite control with the two separate controllers can then be applied in the PM to achieve the desired fast and accurate positioning.     

Synthesis of position,path and function generating 4-bar mechanisms with completely rotatable driving linksSynthese de la position,de la trajectoire et de la generation de fonctions d'un mecanisme a quatre barres articulees

A unified treatment of the synthesis of position, path and function generating mechanisms with completely rotatable input links is presented in this paper. Algebraic-geometrical techniques are used to obtain all proper crank-rocker and drag-link linkage solutions with transmission angles in the range 45° ≤ μ ≤ 135°.     

平面四杆机构刚体导引综合的小波特征参数法

针对傅里叶级数理论不能进行非整周期刚体导引综合的问题,提出了基于Haar小波级数的解决方法,将早期提出的解决平面四杆机构轨迹综合问题的方法扩展到平面四杆机构的刚体导引综合中。通过对刚体转角和其对应基本尺寸型的连杆转角小波系数进行分析,发现了二者的内在联系。在此基础上建立了101 408组基本尺寸型的平面四杆机构刚体导引输出特征参数数据库。将位置输出问题转化为平面四杆机构轨迹综合问题,并给出了计算平面四杆机构实际尺寸和机构安装位置参数的理论公式。利用建立的数据库和理论公式,实现了平面四杆机构非整周期刚体导引综合。以生产线上的输送工件的铰链四杆机构为例,证明了本文方法的有效性和可行性。     

基于TurboC程序的曲柄滑块机构的运动仿真

通过对平面曲柄滑块机构的数学建模,用TurborC编程和参数化绘图,输入曲柄滑块机构的结构参数和运动参数,实现对整个机构运动过程的仿真,并输出滑块的位移、速度、加速度随时间变化的曲线。     

ON THE DYNAMIC MODELING AND CONTROL OF 2-DOF PLANAR PARALLEL MECHANISM WITH FLEXIBLE LINKS

The object of study is about dynamic modeling and control for a 2 degree-of-freedom (DOF) planar parallel mechanism (PM) with flexible links. The kinematic and dynamic equations are established according to the characteristics of mixed rigid and flexible structure. By using the singular perturbation approach (SPA), the model of the mechanism can be separated into slow and fast subsystems. Based on the feedback linearization theory and input shaping technique, the large scale rigid motion controller and the flexible link vibration controller can be designed separately to achieve fast and accurate positioning of the PM.     

平面曲柄摇杆机构可视化性能图谱自动生成与应用软件开发

利用 VB6 .0程序设计语言 ,开发出了能自动生成平面曲柄摇杆机构性能与设计图谱的可视化软件系统。利用该套可视化性能与设计图谱 ,可自动设计满足性能要求的机构基本尺寸 ,可视化自动生成机构运动简图、机构运动线图和机构运动仿真。该图谱是平面曲柄摇杆机构分析与设计的有力工具     

Fuzzy sliding mode controlled slider–crank mechanism using a PM synchronous servo motor drive

The dynamic response of a sliding mode controlled slider–crank mechanism, which is driven by a permanent magnet (PM) synchronous servo motor, is studied in this paper. The rod and crank are assumed to be rigid. The Hamilton’s principle and Lagrange multiplier method are applied to formulate the equation of motion. Reducing the differential-algebraic equations and employing the Runge–Kutta numerical method, the state variable representation is obtained. Moreover, based on the principles of the sliding mode control, a position controller is developed. Then, a simple fuzzy inference mechanism is utilized to estimate the upper bound of uncertainties for the sliding mode controller. Numerical results show that the dynamic behavior of the proposed controller–motor–mechanism system is robust to parametric variation and external disturbance.     

混合驱动平面两自由度七杆机构最优运动规划

详细地分析了混合驱动平面两自由度七杆机构输入与输出运动之间的关系，并在此基础之上提出了闭链机构节点空间内运动规划的步骤与方法。基于改进遗传算法，提出了在闭链机构关节空间内处理具有运动学、动力学约束的最优运动规划问题的新策略。给出了算例并进行了仿真研究。     

5R柔性并联机器人系统运动微分方程

为了描述平面5R柔性并联机器人的运动学和动力学特性,需要建立机器人的运动微分方程。针对刚性活动平台和柔性杆件的运动学耦合特点,改进了一套适用于刚体、柔性体耦合的有限元建模方法,推导出单元弹性广义坐标相对于系统弹性广义坐标的转换矩阵,综合考虑了科氏阻尼、离心刚度和几何非线性的影响,利用运动弹性动力学理论,建立了平面5R柔性并联机器人的运动微分方程,避免了采用运动学和动力学约束方程的弊端,提高了建模精度。计算实例表明,该方程反映了机器人的弹性振动特性,杆件的弹性变形对机器人的运动误差具有重要影响。     

旋转周期为曲柄二整周的平面双曲柄四杆机构

Grashof Neutral机构存在切换点(Change point)位置。通常认为机构在其切换点位置具有运动不确定性,其输入输出角速度比为0/0型不定式。根据运动连续性原理和洛毕达极限法则,首次导出了确定此类机构切换点(Change point)角速度比的解析公式。并通过机构运动分析、仿真,以及机构原型的制作和实验,证明:GrashofNeutral机构旋转通过切换点(Change point)时的运动是完全确定的,具其运动周期为驱动曲柄旋转二整周。特别是,当机构相对杆长差取很小值时,将输出有反向自锁特征和近似长停歇期的间歇运动,具有工业实用价值。     

对称双曲柄齿轮五杆机构连杆曲线及其应用

系统地研究了一种特殊的双曲柄齿轮五杆机构——对称双曲柄齿轮五杆机构。首先分析了齿轮传动比和两齿轮的相对初始相位角对这种机构连杆曲线形状的影响 ,进而分析了该机构实现直线轨迹时的运动特性 ,并给出了这种机构的设计方法 ,最后给出了一些应用实例     

Finite element analysis of high-speed flexible mechanismsAnalyse de mecanismes flexibles de grande vitesse

A procedure is presented for determining the governing equations of a mechanism with physically undamped flexible links and distributed mass, operating at a prescribed input rotational speed. The procedure is illustrated by a detailed analysis of a planar 4-bar angular function generating mechanism. The set of governing equations for the deflections about the rigid body trajectory of mechanism members is derived using the Lagrange equation. These equations are discretized by the finite element method. The equations derived in this paper give a more refined mathematical model by including additional terms as compared to previous methods which represented mechanisms as a sequence of instantaneous structures. The element equations are transformed and assembled to generate the governing differential equations for the mechanism, using a connection procedure suitable for elements which are assumed axially rigid. In this manner a smaller set of global equations than those previously used is obtained.