Disabled people now expect better quality of life with the development of brain computer interfaces (BCIs) and neuroprosthetics. EEG (electroencephalograph) based BCI research for robot arm control mainly concentrates on distinguishing the left/right arm movement. But for controlling artificial arm in real life scenario with greater degrees of freedom, it is essential to classify the left/right arm movement further into different joint movements. In this paper we have classified the raw EEG signal for left and right hand movement, followed by further classification of each hand movement into elbow, finger and shoulder movements. From the two electrodes of interest, namely, C3 and C4, wavelet coefficients, power spectral density (PSD) estimates for the alpha and beta bands and their corresponding powers were selected as the features for this study. These features are further fed into the quadratic discriminant analysis (QDA), linear support vector machine (LSVM) and radial basis function kernelized support vector machine (RSVM) to classify into the intended classes. For left-right hand movement, the maximum classification accuracy of 87.50% is obtained using wavelet coefficient for RSVM classifier. For the multi-class classification, i.e., Finger-Elbow-Shoulder classification the maximum classification accuracy of 80.11% for elbow, 93.26% for finger and 81.12% for shoulder is obtained using the features obtained from power spectral density for RSVM classifier. The results presented in this paper indicates that elbow-finger-shoulder movement can be successfully classified using the given set of features.