There is seldom approach developed for the initial topology design of flexure-based compliant mechanisms.The most commonly-used approaches,which start with an existing rigid-body mechanism,do not consider the performances between different topologies.Moreover,they rely heavily on the rigid-body topology,therefore limit the diversity of compliant mechanisms topology.To obtain the optimal initial topology of such mechanisms directly from problem specifications without referencing to the existing mechanism topologies,a spring-joint method is presented for a restricted class of the serial passive flexure-based compliant mechanisms,which are the building blocks of parallel compliant mechanisms.The topology of the compliant mechanisms is represented by a serial spring-joint mechanism(SSJM)that is a traditional rigid-body mechanism with a torsional spring acting on each joint,and is described by position vectors of the spring-joints.A simplified compliance matrix,determined by the position vectors,is used to characterize the tip of the SSJM kinematically,and is optimized to ensure the desired freedoms of the compliant mechanisms during optimization.The topology optimization problem is formulated as finding out the optimal position of the spring-joints in a blank design domain with an objective function derived from the simplified compliance matrix.In design examples,syntheses of the compliant mechanisms with both single freedom and two decoupled freedoms are presented to illustrate the proposed method.The proposed method provides a new way for the initial design of flexure-based compliant mechanisms. There is seldom approach developed for the initial topology design of flexure-based compliant mechanisms. The most commonly-used approaches, which start with an existing rigid-body mechanism, do not consider the performances between different topologies. Moreover, they rely heavily on the rigid-body topology, therefore limit the diversity of compliant mechanisms topology.To obtain the optimal initial topology of such mechanisms directly from problem specifications without referencing to the existing mechanism topologies, a spring-joint method is presented for a restricted class of the serial passive flexure-based compliant mechanisms, which are the building blocks of parallel compliant mechanisms. The topology of the compliant mechanisms is represented by a serial spring-joint mechanism (SSJM) that is a traditional rigid-body mechanism with a torsional spring acting on each joint , and is described by position vectors of the spring-joints.A simplified compliance matrix, determined by the position ve ctors, is used to characterize the tip of the SSJM kinematically, and is optimized to ensure the desired freedoms of the compliant mechanisms during optimization. topology solution problem is formulated as finding out the optimal position of the spring-joints in a blank design domain with an objective function derived from the simplified compliance matrix. design examples, syntheses of the compliant mechanisms with both single freedom and two decoupled freedoms are presented to the proposed method. proposed method provides a new way for the initial design of flexure- based compliant mechanisms.