The paper presents selected methods used for estimation the unknown geometrical parameters of a spatial mechanism model, used to describe the position and orientation of the end-effector, for example the coordinates of the center points of spherical joints, link dimensions etc. These data are necessary when dealing with computer simulation of any mechanism. The parameters are estimated based on coordinate measurements of selected points, located on the real mechanism links, using a portable manipulator with serial structure composed of 6 revolute joints and a spherical probe, but other techniques of acquiring point coordinates are applicable as well. The described methods can be used in the cases of a disassembled link, an assembled mechanism and redundant data sets. The methods are characterized by accuracy and robustness in the presence of different levels of noise, stability with respect to degenerate data sets, and low computation time. Special attention is paid to the case when the wanted parameters are hard to measure directly. Numerical examples are presented dealing with 5-link mechanism used to guide front wheels of a car.
The paper presents kinematic characteristics of the double 4-link coupler system, used in actual powertrain of low-floor trams (NGT6-Kr). The spatial kinematic model of the couplings was formulated assuming ideal joints and rigid members. The constraints equations of the mechanism were solved iteratively and differentiated to obtain the Jacobian matrix. The mobility and singularity analysis of the coupler mechanism was performed on the basis of the Jacobian matrix.
Kinematic characteristics of the single and double coupler system were analyzed for gross angular and linear axle displacements (misalignments), taking the advantage of the fully nonlinear model. The coupling system was evaluated based on criteria describing homokinetics, balancing and clearance demands, and angular displacements in the joints. These criteria were determined for different design parameters like: coupler proportions, platform shift and angle, middle shaft length.
The paper presents optimization of 5-rod (5-link) suspension mechanism used in passenger cars for independent guiding of the wheels. Selected stiffness coefficients defined for five elastomeric bushings installed in joints of the suspension rods are considered as design variables. Two models with lumped parameters (i.e. elastokinematic and dynamic) of wheel-suspension-car body system are formulated to describe relationships between the design variables and the performance indexes including car active safety and ride comfort, respectively. The multi-criteria goal function is minimized using a deterministic algorithm. The suspension with optimized bushings rates fulfils desired elastokinematic criteria together with a defined dynamic criterion, describing the so-called rolling comfort. An event of car passing over short road bump is considered as dynamic conditions. The numerical example deals with an actual middle-class passenger car with 5-rod suspension at the front driven axle. Estimation of the models parameters and their verification were carried out on the basis of indoor and outdoor experiments. The proposed optimization procedure can be used to improve the suspension design or development cycle.
The paper presents design and experimental verification of platform mechanism with cost-effective wire-based sensors for measuring of spatial displacement or pose of some moving object. This task, also known as spatial tracking, has a very wide application. The proposed mechanism, guided by the moving object, has a parallel structure with two platforms and at least six wire-based sensors for measuring distances between the platform points. Changes of the platform pose cause corresponding changes of the sensors' wire lengths. Forward position problem of an equivalent mechanism model with 6 degrees of freedom is described together with analyses of work space limitations and error propagation in a measurement system. A specific application is illustrated for tracking of a wheel knuckle of 5-link suspension mechanism used in passenger cars. The developed device has the following advantages: it can be installed in a wheel cavity; enables dynamic measurements on the road; is cost-effective. Performance of the latest prototype of the wire-based tracker was verified on the basis of measurements on a test rig, where two other measuring devices were used for comparison purposes.
This paper presents an estimation method for the spatial pose and displacement parameters of multi-rod suspension mechanism, based on measurement results by using wire sensors. Some changes of position and orientation of the platform fixed to wheel knuckle cause corresponding changes of sensors’ cable lengths. The fixation points of the cable sensors are selected with the collision-free conditions taken into account. Numerical example deals with platform poses and positioning of the sensors that satisfy the measurement conditions.