Abstract
This paper discusses the influence of the clearance in joints on the joint reaction forces in mechanisms. By using mathematical programming, the optimal parameters of kinematic chains can be efficiently obtained by using the deterministic approach. However, the situation becomes more sophisticated if random effects of tolerances of the arm lengths and the random pin positions have to be considered. In this work the influence of clearances on joint forces is calculated by using the Taylor approximation and the Monte Carlo method. The implementation of the model is illustrated with two examples. The first example considers a closed loop chain, representing a four-bar mechanism being an actual part of a hydraulic support, employed in mining industry. The second example considers joint reaction forces of car wiper mechanism.
Highlights
Kinematic chains are widely used in industry [1], which is reflected in extensive literature and studies available, see e.g. [2, 3, 4]
Some good examples are the optimal track problem of a closed kinematic chain [6] and the problem related to the impact of tolerances of arm lengths and random pin positions, discussed in [7, 8]
The first one is the kinematic chain with the optimal length of the links, obtained in [6] by employing optimization methods, and the second example is a car wiper mechanism. For both examples the influence of the clearances in the joints on the joint reaction forces is studied. This is achieved by an adequate mathematical model that reflects the effects of tolerances of arm lengths and random pin positions
Summary
Kinematic chains are widely used in industry [1], which is reflected in extensive literature and studies available, see e.g. [2, 3, 4]. The first one is the kinematic chain with the optimal length of the links, obtained in [6] by employing optimization methods, and the second example is a car wiper mechanism For both examples the influence of the clearances in the joints on the joint reaction forces is studied. This is achieved by an adequate mathematical model that reflects the effects of tolerances of arm lengths and random pin positions. It consists of two four-bar mechanisms FEDG and AEDB as shown on Fig. 1b. The car wiper mechanism consists of two four-bar mechanisms ADCB and DGFE as shown in Fig. 2.The clearance in joints on the joint reaction forces will be studied for the ADCB mechanism
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