Today I am going to outline my personal junbi-undo/taiso (preparatory exercises/warm up). Whilst I have not specifically provided what I do (as I regularly change), I have given the complete formula which dictates the types of exercises I utilize, and some key pointers that I follow. In sum, I believe that the routine I have described here ensures that one is well prepared for any karate class, and, if followed, keeping the conclusive tips in mind, will ensure that karateka avoid acquiring stretching-based injuries. OK, so on to the outline...(a) Light aerobic exercises/loosening up: After completion of the opening formalities of the practice session the body is gently prepared for the movements of karate-do via light aerobic exercises and joint articulations. For example, small scale knee rotations, shoulder circles, jogging around the dojo etcetera. The point is to not get worn out but, rather, work up a light sweat and safely free up ones joints; subsequently, this must have the body well prepared for stretching.
(b) Passive static stretches: Contrary to many nowadays, and without allowing the body to cool down, I find that the traditional use of several passive static stretches at this point is very effective; in particular, for the lower body (hip flexors, groin, hamstrings, gluts and quadriceps). For example, stance based stretches, and the classic floor stretches working towards the front, left and right box splits. After completing these stretches, you will probably need to loosen up again; thus, it is always good to utilize some joint rotations at this point. 
(c) Dynamic stretches: These stretches are essentially relaxed leg swings to the front, side, rear and both inside-outward, and outside-inward; furthermore, I practiced arm swings with progressively increasing speed: forward, rearward, and side to side rotating the torso. All of these exercises are not forced. Instead, the range of motion is safely increased according to ones daily condition. Forcing these stretches, besides being potentially hazardous for the body, causes the muscles to tense, which in turn results in the inability to authentically stretch the muscles.* This concludes my preparatory exercises. Following this, one’s body and mind will be well prepared for karate-do training. I would just like to end with a couple of tips. Firstly, stretching should not be painful, it should be a stretch; therefore, take your time and listen to your body. Secondly, try to warm up in comfortable environment, ideally not freezing cold (but, if in cold environment, such as participating in kangeiko, increase the aerobic portion of your preparatory exercises). In my case, here in Aso-shi, unfortunately this is not an option; consequently, it is a case of simply soldiering on... Third and lastly, pertaining to point one, don't compete with others, nor yourself. Some days, perhaps you will be stiff and sore, others you may feel very loose. The preparatory exercises are just that, preparation for training, they are not a measure of your self-improvement or ability in relation to others in your dojo. Injuring yourself because of "overdoing it", during you preparatory exercises, is clearly not smart. Relax, breath, and work according to your daily condition.
Conclusion: I wish you the best of luck in your karate-do training; moreover, that you maintain a healthy body whilst practicing with vigor. On the whole, it is irrefutable that safe, and effective, junbi-undo/taiso is paramount in the on-going advancement of karate-do skills.
© André Bertel. Aso-shi, Kumamoto-ken. Japan (2014).