For theoretical study and engineering application, it is necessary to provide an accurate and simple dynamical model to simulate the multibody mechanical systems with clearance joints and it is also the subject of this article. Based on Lagrange equations of the first kind, a different numerical methodology, the length and rotation angle of the clearance joints are looked as independent coordinates for the first time, is presented in detail. The slider–crank mechanism, with a single or double adjustable revolute clearance joints, is used as a numerical model. A test rig and a simulink model, fully in accordance with the numerical model, are used to measure the velocity, displacement, and acceleration. The numerical results tally with experimental and simulink results reveal that the new methodology, presented in this paper, provides a correct approach to build the dynamical equations of mechanism with clearance joints. Lyapunov exponent is used to analyze the motion status, chaotic or periodic, of the slider. Based on data points, mean absolute deviation (MAD) is applied to judge the dynamical errors, displacement, velocity, and acceleration, of the slider due to clearance joints. With the help of Lyapunov exponent and MAD, the results indicated that various clearance sizes and drive speeds can change the dynamical behaviors of the slider, which is complex but can be predicted in some way.