With the rapid development of mobile Internet techniques and Online-to-offline (O2O) business models, various spatial crowdsourcing (SC) platforms become popular. In particular, the SC platforms, such as Didi taxi and Baidu meal-ordering service, play a significant role in people's daily life. A core issue in SC is task assignment, which is to assign real-time tasks to suitable crowd workers. Existing approaches usually are based on infeasible assumptions and have the following two drawbacks:(1) Existing methods often assume to work on the static scenarios, where the spatio-temporal information of all tasks and workers is known before the assignment is conducted. However, since both tasks and workers dynamically appear and request to be allocated in real time, therefore, existing works are impractical in real applications. (2) Existing studies usually assume that there are only two types of objects, tasks and workers, in SC and ignore the influence of workplace for task assignment. To solve the aforementioned challenges, this paper frames a novel dynamic task assignment problem, called online task assignment for three types of objects in spatial crowdsourcing, which not only includes the three types of objects, namely tasks, workers and workplaces, but also focuses on dynamic scenarios. Moreover, a random-threshold-based algorithm is designed for the new problem and a worst-case competitive analysis is provided for the algorithm. Particularly, to further optimize the algorithm, an adaptive threshold algorithm, which is always close to the best possible effectiveness of the random-threshold-based algorithm, is developed. Finally, the effectiveness and efficiency of the proposed methods are verified through extensive experiments on real dataset and synthetic datasets generated by different distributions.