Misalignment and tolerance are the most common causes of vibrations in machines. An optimum value of tolerance and alignment are desired for a smooth and clear machine process, but difficult to achieve due to manufacturing, assembly and working constraints of the mechanism. Vibration analysis is a study of repetitive motion, in a certain time interval, which involves mathematical modelling, formulation of governing equations and interpretation of vibration response. Misalignment and tolerance incompliance can result in numbers of failures and safety issues, especially for manually operated machines. These problems need to be diagnosed by using vibration analysis for different purposes such as fault detection, vibration response, research and early prevention. This paper provides an insight into the different available methods and fundamentals of vibration analysis that were used to study these issues in a different situation. © 2020, Springer Nature Singapore Pte Ltd.