Purpose This paper focuses on how the producer inspires his cooperative research partner to reduce carbon emission, by developing a menu of incentive contracts both in research and development (R&D) stage and recycling stage. Design/methodology/approach The proposed mechanism combines the researcher with the producer in a two-staged closed-loop system. Based on the concept that the producer takes the environmental responsibility, this paper designs a dynamically updating contract for the producer to encourage low-carbon efforts. Meanwhile, the producer offers a menu of contracts against the asymmetric information, that is, the R&D partner owns private information on his low-carbon R&D capability. According to incentive mechanism, the researcher decides whether to tell the truth and how much effort she would exert in R&D and recycling stages. Findings Discriminating between different types of researchers hurts the producer’s profit. But the updated screening contract can inspire researchers to tell the truth and is beneficial in reducing carbon emissions in the two stages. The results give the optimal solutions of the incentive mechanism. The low-type researcher only obtains reservation profit, whereas the high-type is given more to induce the information. Originality/value This paper proposes a strategy of updating the contract factors for avoiding adverse selection and moral hazard. Considering the environmental responsibility of waste products, the producer would like to encourage low-carbon designs among the R&D partners in a closed-loop supply chain.

The practical algorithm solves real time inverse kinematics of industrial 7R Robot. Here D-H method is used to set up a closed-form 4×4 matrix equation of the 7R Robot, and then sine and cosine of joint angles is transformed to complex exponential form, 10 equations in same form are obtained. We extract the coefficient of every term to construct a 16×16 real number matrix. And the inverse kinematics of 7R Robot can be changed into eigenvalues and eigenvectors problem. For the extra revolute joint of the 7R redundant robot, minimize the condition number of all the solutions, the best one can be obtained. A numerical example shows that the program written in C++ language runs fast enough in the real time control of an industrial robot.

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